From 7907a3fecf9257250f93d6938c16f5f434067b87 Mon Sep 17 00:00:00 2001 From: Danny Staple Date: Wed, 18 Jan 2023 13:57:13 +0000 Subject: [PATCH] Rename folders as per suggestion from Rajat --- {ch-1 => ch-01}/test-fit.drawio | 0 {ch-2 => ch-02}/blink.py | 0 {ch-2 => ch-02}/helloworld.py | 0 {ch-2 => ch-02}/light_led.py | 0 ch-3/Robot.FCStd => ch-03/robot.FCStd | Bin {ch-4 => ch-04}/cutting-template.pdf | Bin {ch-5 => ch-05}/1-tests/motors_test_1_pin.py | 0 .../1-tests/motors_test_1_pin_short.py | 0 .../1-tests/motors_test_all_pins.py | 0 .../1-tests/motors_test_all_pins_short.py | 0 {ch-5 => ch-05}/1-tests/robot.py | 0 .../2-forward-back/motors_backward.py | 0 .../2-forward-back/motors_forward.py | 0 {ch-5 => ch-05}/2-forward-back/robot.py | 0 .../3-turning/motors_1_motor_turn.py | 0 .../3-turning/motors_2_motor_turn.py | 0 {ch-5 => ch-05}/3-turning/robot.py | 0 {ch-5 => ch-05}/4-pwm/1-with_pwm/robot.py | 0 {ch-5 => ch-05}/4-pwm/2-with_helpers/robot.py | 0 {ch-5 => ch-05}/4-pwm/motors_convert_speed.py | 0 .../4-pwm/motors_pwm_drive_slower.py | 0 .../4-pwm/motors_pwm_gentle_turn.py | 0 .../4-pwm/motors_pwm_multispeed.py | 0 {ch-5 => ch-05}/5-path/pwm_drive_square.py | 0 {ch-5 => ch-05}/5-path/robot.py | 0 {ch-6 => ch-06}/0-pio-basic/pio_led_test.py | 0 .../1-simple-input/pio_read_1_pin.py | 0 .../1-simple-input/pio_read_2_pins.py | 0 {ch-6 => ch-06}/2-techniques/debugging_isr.py | 0 {ch-6 => ch-06}/2-techniques/extract_a_bit.py | 0 .../2-techniques/extract_a_bit_explore.py | 0 .../2-techniques/invert_a_register.py | 0 .../2-techniques/pio_counting_down.py | 0 .../2-techniques/pio_counting_up.py | 0 .../2-techniques/pio_debugging_registers.py | 0 .../2-techniques/reversing_a_register.py | 0 .../2-techniques/shift_and_reverse.py | 0 {ch-6 => ch-06}/2-techniques/shift_bits.py | 0 .../pio_one_encoder_when_changed.py | 0 .../pio_two_encoders_when_changed.py | 0 .../pio_encoder_counting.py | 0 {ch-6 => ch-06}/7-demos/encoder_mouse_demo.py | 0 {ch-6 => ch-06}/7-demos/measure_fixed_time.py | 0 {ch-6 => ch-06}/7-demos/pio_encoder.py | 0 {ch-6 => ch-06}/7-demos/robot.py | 0 .../8-exercises/cad exercise/Robot.FCStd | Bin .../8-exercises/drive_fixed_count.py | 0 {ch-7 => ch-07}/BracketDrawing.pdf | Bin {ch-7 => ch-07}/DrillingChassiPlateHoles.pdf | Bin {ch-7 => ch-07}/Robot_simple_brackets.FCStd | Bin {ch-7 => ch-07}/UpperPlateDrawing.pdf | Bin {ch-7 => ch-07}/pimoroni_vl53l1x.FCStd | Bin {ch-7 => ch-07}/robot.FCStd | Bin .../1-single-sensor/read_1_sensor.py | 0 .../2-two-sensors/read_2_sensors.py | 0 {ch-8 => ch-08}/3-avoid/avoid_walls.py | 0 {ch-8 => ch-08}/3-avoid/pio_encoder.py | 0 {ch-8 => ch-08}/3-avoid/robot.py | 0 {ch-8 => ch-08}/3-avoid/varying_wall_avoid.py | 0 .../1-bluetooth-bidirectional/code.py | 0 .../2-read-control-packets/code.py | 0 .../3-random-walk-graph/code.py | 0 .../1-bluetooth-hello-world/code.py | 0 .../2-bluetooth-distance-sensors/code.py | 0 .../pio_encoder.py | 0 .../2-bluetooth-distance-sensors/robot.py | 0 .../3-bluetooth-print-incoming/code.py | 0 {ch-9 => ch-09}/4-bluetooth-teleop/code.py | 0 .../4-bluetooth-teleop/pio_encoder.py | 0 {ch-9 => ch-09}/4-bluetooth-teleop/robot.py | 0 .../5-bluetooth-accelerometer-drive/code.py | 0 .../pio_encoder.py | 0 .../5-bluetooth-accelerometer-drive/robot.py | 0 .../pdfs_of_uniform_sums.py | 22 + ch-13/types_of_randomness/poetry.lock | 777 ++++++++++++++++++ ch-13/types_of_randomness/pyproject.toml | 21 + ch-13/types_of_randomness/randomness.ipynb | 569 +++++++++++++ ch-6/8-exercises/cad exercise/Robot.FCStd1 | Bin 202295 -> 0 bytes 78 files changed, 1389 insertions(+) rename {ch-1 => ch-01}/test-fit.drawio (100%) rename {ch-2 => ch-02}/blink.py (100%) rename {ch-2 => ch-02}/helloworld.py (100%) rename {ch-2 => ch-02}/light_led.py (100%) rename ch-3/Robot.FCStd => ch-03/robot.FCStd (100%) rename {ch-4 => ch-04}/cutting-template.pdf (100%) rename {ch-5 => ch-05}/1-tests/motors_test_1_pin.py (100%) rename {ch-5 => ch-05}/1-tests/motors_test_1_pin_short.py (100%) rename {ch-5 => ch-05}/1-tests/motors_test_all_pins.py (100%) rename {ch-5 => ch-05}/1-tests/motors_test_all_pins_short.py (100%) rename {ch-5 => ch-05}/1-tests/robot.py (100%) rename {ch-5 => ch-05}/2-forward-back/motors_backward.py (100%) rename {ch-5 => ch-05}/2-forward-back/motors_forward.py (100%) rename {ch-5 => ch-05}/2-forward-back/robot.py (100%) rename {ch-5 => ch-05}/3-turning/motors_1_motor_turn.py (100%) rename {ch-5 => ch-05}/3-turning/motors_2_motor_turn.py (100%) rename {ch-5 => ch-05}/3-turning/robot.py (100%) rename {ch-5 => ch-05}/4-pwm/1-with_pwm/robot.py (100%) rename {ch-5 => ch-05}/4-pwm/2-with_helpers/robot.py (100%) rename {ch-5 => ch-05}/4-pwm/motors_convert_speed.py (100%) rename {ch-5 => ch-05}/4-pwm/motors_pwm_drive_slower.py (100%) rename {ch-5 => ch-05}/4-pwm/motors_pwm_gentle_turn.py (100%) rename {ch-5 => ch-05}/4-pwm/motors_pwm_multispeed.py (100%) rename {ch-5 => ch-05}/5-path/pwm_drive_square.py (100%) rename {ch-5 => ch-05}/5-path/robot.py (100%) rename {ch-6 => ch-06}/0-pio-basic/pio_led_test.py (100%) rename {ch-6 => ch-06}/1-simple-input/pio_read_1_pin.py (100%) rename {ch-6 => ch-06}/1-simple-input/pio_read_2_pins.py (100%) rename {ch-6 => ch-06}/2-techniques/debugging_isr.py (100%) rename {ch-6 => ch-06}/2-techniques/extract_a_bit.py (100%) rename {ch-6 => ch-06}/2-techniques/extract_a_bit_explore.py (100%) rename {ch-6 => ch-06}/2-techniques/invert_a_register.py (100%) rename {ch-6 => ch-06}/2-techniques/pio_counting_down.py (100%) rename {ch-6 => ch-06}/2-techniques/pio_counting_up.py (100%) rename {ch-6 => ch-06}/2-techniques/pio_debugging_registers.py (100%) rename {ch-6 => ch-06}/2-techniques/reversing_a_register.py (100%) rename {ch-6 => ch-06}/2-techniques/shift_and_reverse.py (100%) rename {ch-6 => ch-06}/2-techniques/shift_bits.py (100%) rename {ch-6 => ch-06}/3-change-conditions/pio_one_encoder_when_changed.py (100%) rename {ch-6 => ch-06}/3-change-conditions/pio_two_encoders_when_changed.py (100%) rename {ch-6 => ch-06}/4-quadrature-encoding/pio_encoder_counting.py (100%) rename {ch-6 => ch-06}/7-demos/encoder_mouse_demo.py (100%) rename {ch-6 => ch-06}/7-demos/measure_fixed_time.py (100%) rename {ch-6 => ch-06}/7-demos/pio_encoder.py (100%) rename {ch-6 => ch-06}/7-demos/robot.py (100%) rename {ch-6 => ch-06}/8-exercises/cad exercise/Robot.FCStd (100%) rename {ch-6 => ch-06}/8-exercises/drive_fixed_count.py (100%) rename {ch-7 => ch-07}/BracketDrawing.pdf (100%) rename {ch-7 => ch-07}/DrillingChassiPlateHoles.pdf (100%) rename {ch-7 => ch-07}/Robot_simple_brackets.FCStd (100%) rename {ch-7 => ch-07}/UpperPlateDrawing.pdf (100%) rename {ch-7 => ch-07}/pimoroni_vl53l1x.FCStd (100%) rename {ch-7 => ch-07}/robot.FCStd (100%) rename {ch-8 => ch-08}/1-single-sensor/read_1_sensor.py (100%) rename {ch-8 => ch-08}/2-two-sensors/read_2_sensors.py (100%) rename {ch-8 => ch-08}/3-avoid/avoid_walls.py (100%) rename {ch-8 => ch-08}/3-avoid/pio_encoder.py (100%) rename {ch-8 => ch-08}/3-avoid/robot.py (100%) rename {ch-8 => ch-08}/3-avoid/varying_wall_avoid.py (100%) rename {ch-9 => ch-09}/1-bluetooth-basics/1-bluetooth-bidirectional/code.py (100%) rename {ch-9 => ch-09}/1-bluetooth-basics/2-read-control-packets/code.py (100%) rename {ch-9 => ch-09}/1-bluetooth-basics/3-random-walk-graph/code.py (100%) rename {ch-9 => ch-09}/1-bluetooth-hello-world/code.py (100%) rename {ch-9 => ch-09}/2-bluetooth-distance-sensors/code.py (100%) rename {ch-9 => ch-09}/2-bluetooth-distance-sensors/pio_encoder.py (100%) rename {ch-9 => ch-09}/2-bluetooth-distance-sensors/robot.py (100%) rename {ch-9 => ch-09}/3-bluetooth-print-incoming/code.py (100%) rename {ch-9 => ch-09}/4-bluetooth-teleop/code.py (100%) rename {ch-9 => ch-09}/4-bluetooth-teleop/pio_encoder.py (100%) rename {ch-9 => ch-09}/4-bluetooth-teleop/robot.py (100%) rename {ch-9 => ch-09}/5-bluetooth-accelerometer-drive/code.py (100%) rename {ch-9 => ch-09}/5-bluetooth-accelerometer-drive/pio_encoder.py (100%) rename {ch-9 => ch-09}/5-bluetooth-accelerometer-drive/robot.py (100%) create mode 100644 ch-13/types_of_randomness/pdfs_of_uniform_sums.py create mode 100644 ch-13/types_of_randomness/poetry.lock create mode 100644 ch-13/types_of_randomness/pyproject.toml create mode 100644 ch-13/types_of_randomness/randomness.ipynb delete mode 100644 ch-6/8-exercises/cad exercise/Robot.FCStd1 diff --git a/ch-1/test-fit.drawio b/ch-01/test-fit.drawio similarity index 100% rename from ch-1/test-fit.drawio rename to ch-01/test-fit.drawio diff --git a/ch-2/blink.py b/ch-02/blink.py similarity index 100% rename from ch-2/blink.py rename to ch-02/blink.py diff --git a/ch-2/helloworld.py b/ch-02/helloworld.py similarity index 100% rename from ch-2/helloworld.py rename to ch-02/helloworld.py diff --git a/ch-2/light_led.py b/ch-02/light_led.py similarity index 100% rename from ch-2/light_led.py rename to ch-02/light_led.py diff --git 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a/ch-6/3-change-conditions/pio_one_encoder_when_changed.py b/ch-06/3-change-conditions/pio_one_encoder_when_changed.py similarity index 100% rename from ch-6/3-change-conditions/pio_one_encoder_when_changed.py rename to ch-06/3-change-conditions/pio_one_encoder_when_changed.py diff --git a/ch-6/3-change-conditions/pio_two_encoders_when_changed.py b/ch-06/3-change-conditions/pio_two_encoders_when_changed.py similarity index 100% rename from ch-6/3-change-conditions/pio_two_encoders_when_changed.py rename to ch-06/3-change-conditions/pio_two_encoders_when_changed.py diff --git a/ch-6/4-quadrature-encoding/pio_encoder_counting.py b/ch-06/4-quadrature-encoding/pio_encoder_counting.py similarity index 100% rename from ch-6/4-quadrature-encoding/pio_encoder_counting.py rename to ch-06/4-quadrature-encoding/pio_encoder_counting.py diff --git a/ch-6/7-demos/encoder_mouse_demo.py b/ch-06/7-demos/encoder_mouse_demo.py similarity index 100% rename from ch-6/7-demos/encoder_mouse_demo.py rename to ch-06/7-demos/encoder_mouse_demo.py diff --git a/ch-6/7-demos/measure_fixed_time.py b/ch-06/7-demos/measure_fixed_time.py similarity index 100% rename from ch-6/7-demos/measure_fixed_time.py rename to ch-06/7-demos/measure_fixed_time.py diff --git a/ch-6/7-demos/pio_encoder.py b/ch-06/7-demos/pio_encoder.py similarity index 100% rename from ch-6/7-demos/pio_encoder.py rename to ch-06/7-demos/pio_encoder.py diff --git a/ch-6/7-demos/robot.py b/ch-06/7-demos/robot.py similarity index 100% rename from ch-6/7-demos/robot.py rename to ch-06/7-demos/robot.py diff --git a/ch-6/8-exercises/cad exercise/Robot.FCStd b/ch-06/8-exercises/cad exercise/Robot.FCStd similarity index 100% rename from ch-6/8-exercises/cad exercise/Robot.FCStd rename to ch-06/8-exercises/cad exercise/Robot.FCStd diff --git a/ch-6/8-exercises/drive_fixed_count.py b/ch-06/8-exercises/drive_fixed_count.py similarity index 100% rename from ch-6/8-exercises/drive_fixed_count.py rename to ch-06/8-exercises/drive_fixed_count.py diff --git a/ch-7/BracketDrawing.pdf b/ch-07/BracketDrawing.pdf similarity index 100% rename from ch-7/BracketDrawing.pdf rename to ch-07/BracketDrawing.pdf diff --git a/ch-7/DrillingChassiPlateHoles.pdf b/ch-07/DrillingChassiPlateHoles.pdf similarity index 100% rename from ch-7/DrillingChassiPlateHoles.pdf rename to ch-07/DrillingChassiPlateHoles.pdf diff --git a/ch-7/Robot_simple_brackets.FCStd b/ch-07/Robot_simple_brackets.FCStd similarity index 100% rename from ch-7/Robot_simple_brackets.FCStd rename to ch-07/Robot_simple_brackets.FCStd diff --git a/ch-7/UpperPlateDrawing.pdf b/ch-07/UpperPlateDrawing.pdf similarity index 100% rename from ch-7/UpperPlateDrawing.pdf rename to ch-07/UpperPlateDrawing.pdf diff --git a/ch-7/pimoroni_vl53l1x.FCStd b/ch-07/pimoroni_vl53l1x.FCStd similarity index 100% rename from ch-7/pimoroni_vl53l1x.FCStd rename to ch-07/pimoroni_vl53l1x.FCStd diff --git a/ch-7/robot.FCStd b/ch-07/robot.FCStd similarity index 100% rename from ch-7/robot.FCStd rename to ch-07/robot.FCStd diff --git a/ch-8/1-single-sensor/read_1_sensor.py b/ch-08/1-single-sensor/read_1_sensor.py similarity index 100% rename from ch-8/1-single-sensor/read_1_sensor.py rename to ch-08/1-single-sensor/read_1_sensor.py diff --git a/ch-8/2-two-sensors/read_2_sensors.py b/ch-08/2-two-sensors/read_2_sensors.py similarity index 100% rename from ch-8/2-two-sensors/read_2_sensors.py rename to ch-08/2-two-sensors/read_2_sensors.py diff --git a/ch-8/3-avoid/avoid_walls.py b/ch-08/3-avoid/avoid_walls.py similarity index 100% rename from ch-8/3-avoid/avoid_walls.py rename to ch-08/3-avoid/avoid_walls.py diff --git a/ch-8/3-avoid/pio_encoder.py b/ch-08/3-avoid/pio_encoder.py similarity index 100% rename from ch-8/3-avoid/pio_encoder.py rename to ch-08/3-avoid/pio_encoder.py diff --git a/ch-8/3-avoid/robot.py b/ch-08/3-avoid/robot.py similarity index 100% rename from ch-8/3-avoid/robot.py rename to ch-08/3-avoid/robot.py diff --git a/ch-8/3-avoid/varying_wall_avoid.py 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ch-09/5-bluetooth-accelerometer-drive/code.py diff --git a/ch-9/5-bluetooth-accelerometer-drive/pio_encoder.py b/ch-09/5-bluetooth-accelerometer-drive/pio_encoder.py similarity index 100% rename from ch-9/5-bluetooth-accelerometer-drive/pio_encoder.py rename to ch-09/5-bluetooth-accelerometer-drive/pio_encoder.py diff --git a/ch-9/5-bluetooth-accelerometer-drive/robot.py b/ch-09/5-bluetooth-accelerometer-drive/robot.py similarity index 100% rename from ch-9/5-bluetooth-accelerometer-drive/robot.py rename to ch-09/5-bluetooth-accelerometer-drive/robot.py diff --git a/ch-13/types_of_randomness/pdfs_of_uniform_sums.py b/ch-13/types_of_randomness/pdfs_of_uniform_sums.py new file mode 100644 index 0000000..6eaa72b --- /dev/null +++ b/ch-13/types_of_randomness/pdfs_of_uniform_sums.py @@ -0,0 +1,22 @@ +import matplotlib.pyplot as plt +import numpy as np +import random + +population_size = 100000 + + +def make_uniform_series_plot(n): + uniform_series = np.array( + [sum(random.uniform(0, 1) for _ in range(n))/n for _ in range(population_size)]) + plt.hist(uniform_series, bins=200, histtype='step', label=f"n={n}") + +make_uniform_series_plot(1) +make_uniform_series_plot(2) +make_uniform_series_plot(3) +make_uniform_series_plot(4) +make_uniform_series_plot(8) +make_uniform_series_plot(12) +plt.title(f"Uniform series") + +plt.legend() +plt.show() diff --git a/ch-13/types_of_randomness/poetry.lock b/ch-13/types_of_randomness/poetry.lock new file mode 100644 index 0000000..6c7187e --- /dev/null +++ b/ch-13/types_of_randomness/poetry.lock @@ -0,0 +1,777 @@ +[[package]] +name = "async-timeout" +version = "4.0.2" +description = "Timeout context manager for asyncio programs" +category = "main" +optional = false +python-versions = ">=3.6" + +[[package]] +name = "black" +version = "22.12.0" +description = "The uncompromising code formatter." +category = "dev" +optional = false +python-versions = ">=3.7" + +[package.dependencies] +click = ">=8.0.0" +mypy-extensions = ">=0.4.3" +pathspec 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+[tool.poetry] +name = "modelling-space" +version = "0.1.0" +description = "" +authors = ["Danny Staple "] +readme = "README.md" +packages = [{include = "modelling_space"}] + +[tool.poetry.dependencies] +python = "^3.9" +matplotlib = "3.6.1" +numpy = "1.23.4" +bleak = "0.19.0" + + +[tool.poetry.group.dev.dependencies] +black = "^22.10.0" + +[build-system] +requires = ["poetry-core"] +build-backend = "poetry.core.masonry.api" diff --git a/ch-13/types_of_randomness/randomness.ipynb b/ch-13/types_of_randomness/randomness.ipynb new file mode 100644 index 0000000..07238b1 --- /dev/null +++ b/ch-13/types_of_randomness/randomness.ipynb @@ -0,0 +1,569 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "from matplotlib import pyplot as plt\n", + "import numpy as np\n", + "import random" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Dice" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(array([1., 2., 3., 4., 5., 6., 5., 4., 3., 2., 1.]),\n", + " array([ 2. , 2.90909091, 3.81818182, 4.72727273, 5.63636364,\n", + " 6.54545455, 7.45454545, 8.36363636, 9.27272727, 10.18181818,\n", + " 11.09090909, 12. ]),\n", + " [])" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# dice combinations for 2 dice\n", + "dice_combinations = [(i, j) for i in range(1, 7) for j in range(1, 7)]\n", + "# sum these combinations\n", + "dice_sums = [sum(combination) for combination in dice_combinations]\n", + "plt.hist(dice_sums, bins=11, histtype='step', label=f\"2 dice\")\n" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(array([ 1., 3., 6., 10., 15., 21., 25., 27., 0., 27., 25., 21., 15.,\n", + " 10., 6., 3., 1.]),\n", + " array([ 3. , 3.88235294, 4.76470588, 5.64705882, 6.52941176,\n", + " 7.41176471, 8.29411765, 9.17647059, 10.05882353, 10.94117647,\n", + " 11.82352941, 12.70588235, 13.58823529, 14.47058824, 15.35294118,\n", + " 16.23529412, 17.11764706, 18. ]),\n", + " [])" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# dice combinations for 3 dice\n", + "dice_combinations = [(i, j, k) for i in range(1, 7) for j in range(1, 7) for k in range(1, 7)]\n", + "# sum these combinations\n", + "dice_sums = [sum(combination) for combination in dice_combinations]\n", + "plt.hist(dice_sums, bins=17, histtype='step', label=f\"3 dice\")" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "# Generalised dice combinations for n dice\n", + "def count_ways_to_make_sum_with_dice(dice_count, expected_sum):\n", + " if expected_sum < dice_count or expected_sum > 6 * dice_count:\n", + " return 0\n", + " if dice_count == 1:\n", + " return 1\n", + " return sum(count_ways_to_make_sum_with_dice(dice_count - 1, expected_sum - i)\n", + " for i in range(1, 7))\n" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "dice_sums = [count_ways_to_make_sum_with_dice(2, i) for i in range(1, 14)]\n", + "plt.plot(np.arange(1, 14), dice_sums, label=f\"2 dice\")\n" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "n = 3\n", + "dice_sums = [count_ways_to_make_sum_with_dice(n, i) for i in range(1, n*7)]\n", + "plt.plot(np.arange(1, n*7), dice_sums, label=f\"{n} dice\")" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "n = 4\n", + "dice_sums = [count_ways_to_make_sum_with_dice(n, i) for i in range(1, n*7)]\n", + "plt.plot(np.arange(1, n*7), dice_sums, label=f\"{n} dice\")" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "n = 8\n", + "dice_sums = [count_ways_to_make_sum_with_dice(n, i) for i in range(1, n*7)]\n", + "plt.plot(np.arange(1, n*7), dice_sums, label=f\"{n} dice\")" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [], + "source": [ + "population_size = 100000\n", + "def make_uniform_series_plot(n):\n", + " uniform_series = np.array(\n", + " [sum(random.uniform(0, 1) for _ in range(n))/n for _ in range(population_size)])\n", + " plt.hist(uniform_series, bins=200, histtype='step', label=f\"n={n}\")" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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dt8PDwxEeHt7SS+FRfn4+7rvvPqxduxaTJk1q9/cTEVHncAlJJYxGI7KysvD3v/8dAwcORHp6OgYMGODMYWmrbt26tem8sLAwXLt2zeVYVFQUAGDgwIEux++8804UFha6HLt69Spuu+025+133nkHP/nJT5oEGsXFxbj33nsxZswY7Nixo8UxzZ49Gz/84Q+dtw0GA1JTU1tcwnHPdTEYDM5ADOjYEtLnn3+OiRMnYtGiRXj88cdbHDORQOiDRETSYACjIgaDAXfffTfWrVuHf/3rXwgICMDBgwdhNpsRFRWF3Nxc57m3bt1y6fjdEn9/f9TV1bkcGz58OEpKSlyCmL59+yI6Ohrnz593ObegoMC5rCXIz8/H8OHDnbfffvtt3HfffS7nWK1W3HPPPUhISEBmZqbLclVL+vbtK9kW6vXr1zubkzb3IXbu3Dnce++9mDt3Lp5++mlJxkD6NS39pLNSLxG1D5eQVCI3NxfZ2dmYNGkSwsPDkZubi8uXLzuTbB9++GFs3LgR/fr1wx133IHnn38eNputTY/dt29fZGdn4+6770ZgYCBCQkIwfPhwhIWF4aOPPsK0adMAOAKolStXYu3atRg2bBji4+Oxe/dufPnll3jzzTedj1dVVYW8vDw888wzABzJv//85z/xzjvvOM8Rgpc+ffrgueeew+XLl533iXNxvK09S0j5+fmYMGECkpOTsWLFCpSUlABwzI6JZ5tIBipqLeAu32rH4Biz3MMgUh0GMO58VcWznc8THByMEydOIC0tDRUVFejTpw+2bNmCKVOmAAAeffRRXLp0CXPnzoWfnx/mz5+Pn/3sZ7DbW7+627JlC1asWIGdO3ciJiYGX3/9NYxGI+bNm4d9+/Y5AxgAWL58OW7cuIFHHnkEV69exbBhw5CVleWytPP222+jd+/e+PGPfwwAePfddzFq1CiEhYU5z8nKysKFCxdw4cKFJhV7W2oWKqc333wTly9fxt69e7F3717ncWHrOcmgva0FxNW2VVAJm4iaZ2hQ6l+LTqqoqIDZbIbdbkdwcLDLfTdu3MDFixcRFxfXmJOhwUq8Qh0UoQ5Me5WUlGDQoEH49NNPmywRteSuu+7CQw895Gw/8F//9V8YO3YsHnvssQ6NQ808/qzpnXvLDnEgYSsCCnMcRR4XHW9bTSbh8dwDkuIzwI7xjY/j/jvug0rYQidqsdl39cbejxtzxrbPSUDyIN/NOhIpXUt/v8U4AyMQ91jxFYVfAUZGRuKVV15BYWFhmwOY8vJypKSk4Je//KXz2NixY11uk455ulAQAgmg8b72tAJw71TdHHG1XsDrlbA9BS9iE+4Ix5Evy9hKgKiDGMCItfWNUEfc+yO1JiwsrMlMix5nXqgZ7iX/hZYahTmO+4X7eidK+7toK2pctnVvFdLcDE4ntZacG23hjBxRZzCA0TBfNzskajOh5L+Qw3Lg+/o//kHSBy/iRo/CzI6nJpA+aq5abLvh1ccn0gsGMEQkH/elW28sq4pnfYTgSHg+4b5xKx2JwD5ornpV1OCRiDqOAQwRyctXS7dh/Zt/HjOXjonURteF7DS6AYsUhD9jRETeocsARigvL+7VQ+QNws+Ye0sDUggVF8Aj0jtdLiEZjUZYLBaUlZUBAIKCgmAwGGQeFWlJQ0MDqqqqUFZWBovF4tJQUrfEO4F8yVOQ0t4CeBIaHBOMM0U2nz0fkVbpMoABGsvVC0EMkTdYLBaftkZQLHH9F18FDC0FKeLkYfGuJC87tGwsex8RSUS3AYzBYEBUVBTCw8NRW1sr93BIg/z9/TnzIvC0E8jb3IMU9+cUJw97IYAJ6RYg+WMSUSPdBjACo9HIPzJEvtLSTiBvaO8Op/ICybZyCxV2H5pwO7YeudDpxyMiV7oPYIjIC7xU3dZrxAX1JC5oF81WAURewQCGiKTlnu8i9DlSMmG5SWgkWZijrgCMSIcYwBCRtDxVt1UDIVBxb23QydmYkG4BMPkbnV8TkTQYwBCRdwjVbeXYOt1R4sRfodFkJ9sLxFhM+PDR8c6v3U1LP4lDy8ZicIy5w89BpEcMYIioY4Q8F8DzUounRo0+rLfSYV5obeApcBFjEEPUfgxgiKj9xHkugOelFnMv7zdq1JB8q50BDFE7MIAhovYT13UBml9q8VWjRiLSHQYwRNRxYf3lHoH3SVgbBoBzlmVwNGdbiDpDl80ciYhaJc7h2TbKsWwmgcExZny9cSqXi4g6iQEMEZEnwo6klJ2O5TIvbwe/Ulnj1ccn0hoGMEREzbHE+myZbPP752G1VfvkuYi0gDkwRNQ24vYALZ2jprov7eWpRYKEbROuVda0uuWaiBwYwBBR69zbAwi7j8Ts3wKZUxrPUUPNl/Zw//cJLRLc2ibkVwZjWvpJbEwZIu94iTSOS0hE1Dpxe4Dm8kHEW6slbIaoGJ5eAw/H8q12AMCJry63+HDiFgNrpw/0+vCJtIYzMETUduY2BCVh/bUXvIh5eg08HPvb2RKY/I3N9j8Stxi4xgReonbjDAwRkYSCqi9hkOEiolGOjDkJLea0xFhMzHkh6iDOwBARScX+LX564n/wX4HVqGoIRFHDSAC3yT0qIk3iDAwRkVSqrqBLXTW23rofQYabMN64KveIiDSLAQwRkcSsDR2fdbHaqlkPhqgNuIRERNQRXqh3Y7VV44GMHADAh4+OZ34MUQsYwBBRy7RenK69xD2SAElr3izek+f8mkXtiFrGAIaImudewE5rxek6wtzLUedGqIUT1NP5tdVWjRgZh0akJwxgiKh54uJ0vRO93tBQNSyxrrVuGMAQ+RyTeImodVovTkdEqsMAhojaz14k9wgUKSiAk9pEvsIAhojaTkhgPbGZOTEehAT5u9wONvk3cyYRdRYvF4jIkaxbdcURkLS0VGSJbUxgFc5lXkwTc+7qA+QB4d0D23Q+674QtR8DGCK9c99p9Is9QNiA5gMZ9wRWasJ9JqY1bOZI1H5cQiLSO2Gn0eSNjtt7ZzgCGhvzXIhIuRjAEJFD70TH8lDKTkdAw6UhIlIwLiERUSPmtMhicIxZ7iEQqQ5nYIhIGtxa3WGDY8w4tGys3MMgUhUGMETUOdxaTUQykDyAqaurwxNPPIG4uDiYTCb88Ic/xFNPPYWGhgbnOQ0NDVizZg2ioqJgMpmQlJSEr776yuVxrl69ilmzZiE4OBgWiwULFizA9evXpR4uEXWWsLV60XHHZ+5QalReABSfaVNCdEi3AO+Ph0hDJA9gnn32Wbz88st48cUX8cUXX+DZZ5/Fpk2bkJ6e7jxn06ZN2Lp1KzIyMpCbm4tu3bohOTkZN27ccJ4za9YsnDt3DllZWTh06BBOnDiBRYsWST1cIpKCJRaIjmfw8r1bXUMbO1bvGN+mXV0xFhNWJg/w0QiJ1E/yAObUqVO47777MHXqVPTt2xc///nPMWnSJJw+fRqAY/YlLS0Njz/+OO677z4MHToUr732GoqLi/HWW28BAL744gscPnwYf/rTnzB69GiMHTsW6enpeP3111FcXCz1kImIJHH95i0AQG336MZZqXbs6hrf/zZvD5FIMyQPYMaMGYPs7GwUFBQAAD777DOcPHkSU6ZMAQBcvHgRJSUlSEpKcn6P2WzG6NGjkZOTAwDIycmBxWLBiBEjnOckJSXBz88Pubm5Hp/35s2bqKiocPkgIpJMG5KUX/3oawDftxAQZqXC+rf5KZjMS9R2km+jXrVqFSoqKnDHHXfAaDSirq4OTz/9NGbNmgUAKCkpAQBERES4fF9ERITzvpKSEoSHh7sOtEsXhIaGOs9xt2HDBqxbt07qfw6RfpUXyD0CZWhDknLZ9ZsQv2O1tYUAEXWc5AHMn//8Z+zbtw/79+/HoEGDcObMGSxfvhzR0dGYO3eu1E/ntHr1aqxYscJ5u6KiArGxXI8najfhD/aBhY7bet9Z5Kn/k5uK6lqEe/jWzpiWfhKHlo1ljRiiZkgewKxcuRKrVq3CzJkzAQBDhgzBN998gw0bNmDu3LmIjIwEAJSWliIqKsr5faWlpYiPjwcAREZGoqyszOVxb926hatXrzq/311gYCACA3nVQ9Rp4j/YQOsNHvVApv5P+VY7AxiiZkieA1NVVQU/P9eHNRqNqK+vBwDExcUhMjIS2dnZzvsrKiqQm5uLxMREAEBiYiJsNhvy8vKc5xw5cgT19fUYPXq01EMmIndC/gZ3FhGRQkk+AzN9+nQ8/fTT6N27NwYNGoR//etfeP755zF//nwAgMFgwPLly/GHP/wB/fr1Q1xcHJ544glER0fj/vvvBwDceeedmDx5MhYuXIiMjAzU1tZi6dKlmDlzJqKjo6UeMhEREamM5AFMeno6nnjiCfzv//4vysrKEB0djcWLF2PNmjXOcx577DFUVlZi0aJFsNlsGDt2LA4fPoyuXbs6z9m3bx+WLl2KiRMnws/PDzNmzMDWrVulHi4RkW+Ik6JbWJaz2qqdX7O4HVHzJA9gevTogbS0NKSlpTV7jsFgwPr167F+/fpmzwkNDcX+/fulHh6RftmKWkxEJS9xT4oGHLebqVp8rbLG+XWMxeSLERKpErtRE+mBrchRDba2qsU/nuQF7knR5QWOYKbqCv8PiDqBzRyJ9KDqiiN4GbfStSqsrYj1Xjop32rHw6+fafkkcVJ0c4XtbEVA8RkEVV+SeIRE2sQZGCI9MYuu+N1nZfRc66UT8q1259cPTbgd+EcHHkT0f/FTowkb8SyKESbdIIk0iDMwRHolzMqk7OSSkly+n3VBYY5zhqxLXTVCDN/JPTIixeMMDJEeiZeNwvozeJGD/Vsgc4ojcAEcs2BR8bIOiUhNGMAQqYUUu4jYJkA5Lp1pnAEL6+/4f/g+N+l2gxXXGnrIOz4ihWMAQ6QGUu0iMvdimwC5uTeH7J3o8n9Q38WEP+IlVDUEouj6SABsJUDkCQMYIjUQ7yI6sblzW3Bl6utD32upOaQlFn5LP0HRZ9mIPfowjDeuyjdOIoVjAEOkJuY2Bh7CchPAJSIlaimItMTipuV2346HSIUYwBBpjXi5CXAsU6TslHdMREQSYwBDpDXi7dFAY9VXUiWhNxLbChC5YgBDpFXNVXwlSYkbLgYFSvuW+u+y61j+5nEAwIePjmcQQyTCAIaIqIPEnaMBIMTkL8njBn//OFuPXEBIQw+EGL5D9TfdAfRhAjbR9xjAEGmBuEYM+YTVVo2kLcdRXVuHQQZpHzu8eyAAIMZQjr8ErEeQ4SZwEGzESSTCVgJEaick7e4Y7/hs/1buEenCtcoaVNfWefU5QgzXEWS4iYdr/hdF9/7RtREnkc4xgCFSKqFPjq2o5fOa6zRNvmdv5f+qgy40xHBrNZEbLiERKZF75d2Ja1r/npZqxHjpDys5XGvogfouJvgJ1XXlXMqTouUEkQowgCFSImFWZfJGIHs9cHhVx/4wupetZ46MVxQjDF89cAQDetTIGzhI1XKCSAUYwBApWe9E17Lz7V0eaqlsPUmqtnsMEC1t36IYw+X2fYOULSeIFI4BDJHSicvOdyS/hb2P1CeoJ+q7mPAQ3kJVQ2D7O1O3teUEkYoxgCEiUhpLLMoe/AdSd2bhUm03FCNM7hERKQ4DGCIiBYrs3Q9bH+2FfKsdi/fkwV5dK/eQiBSF26iJ1MxWBJQXyD0KgmtLAanEWEwYHGOGyd+IZ977QvLHJ1IzBjBEaiXsODmwkDuMZLYyeYDX+hTFWEzImJOAG7fqvfL4RGrFJSQitRJ3ne6dyAJ2MurphdkXXz4+kRpxBoZI7cL6c5cREekOAxgirWHVXZ8bHCNt/Rciah0DGCKtYNVdWRxaNpYBDJEMmANDpEaedh6x6q5P5FvtmJZ+EhtThsgzgPIC/v8SgQEMkboIsywHFjpuu8+0sOqu1+Vb7Y7PxXafPq+zYaSw64x9jkjnGMAQqYl4lgXglbiOOBtG3sx3BLDCzwBn3EinGMAQqQ1nWXSrtnsM0KPGccP+LZA5pbHz9C/2AFVX5R0gkQ8xiZeIqAP2flwo7wCEOkCTN34/oBksaki6whkYIiI1653YdFmRRQ1JBzgDQ0TUDlcqa2R77mnpJ3Hh8vWmd1higeh4xweXF0knGMAQEbWR1VaNze+fl3UM/y77PoBpS8HC8gJHzywiDeISEhFRG12TcfZFcDMgpPWCheLt9i1tubYVcRcTqRYDGCKidnpowu3YeuSCLM9dZYpqvWChsN2+MKdxy7X7eUI3c2EXE+vKkMpwCYmIqJ0GxZhh8jfC5G9EiBydooWcl5YCDkuso9GnmK0IKD7TOPNSWwWMW+n4zMRfUhnOwBApifCHxVOrAFKMGIsJHz463vm1t4mDpOrauo49iPuMS8pOx3EzZ11InTgDQ6QEtiLgwoeOPzA7xrOeh8LkW+3ou+o9ZxsBwBG4+CJ4EZ5r7fSBAIB1734Oq626/Q/CGRfSGM7AEMnJVgSUnwfemNN4ZTz7r0BQGBMrFUQIXD74vFS2MZj8jc6v8632jgdPnHEhjWAAQyQX9yn92X8FwgYwaFGwI1+WAXBspx4cY5ZtHIv35OGjVRN8NgNEpEQMYIjkIkzpp+x0VFNl4KIaSthOfa2yhgEM6RpzYIjkYCtqTNQN68/ghYionRjAEPmasHTERF3VkGWrdDNm39Vb7iEQKQKXkIh8jUtHqsOlGiLl4QwMkVy4dKRacibwEpEDAxgionbYmDKEAQyRAjCAISIiItVhDgwRkdaxNQVpEAMYIiKtCurp2Ol2YKHjdku73oQghxWgSSUYwBB5i9CYkX8QSAJC3s3g6Hbk31higdTTjX2Pgno2fm0vajzmHuSknubPLCkeAxgib3BvE8A/CNRJg2PM+HrjVJeGkm1iiW36s+cfBJzY7PgcNawxyCkvcAQyVVf480qKxwCGyBvEnX9PbAYKcxqvfJmPQHISz8qIZwcZsJDKMIAh8qaoeNfpeQEr8JKcPM3KNIdLoaRQDGCIvMncyzUHQcA/BqqlqxowXAolBWMAQ+Rt7bnaJUU7tGysvgIY96VQ5saQgnilkJ3VasXs2bPRs2dPmEwmDBkyBP/85z+d9zc0NGDNmjWIioqCyWRCUlISvvrqK5fHuHr1KmbNmoXg4GBYLBYsWLAA169f98ZwiYjInbhjuplBCymP5AHMtWvXcPfdd8Pf3x9///vf8fnnn2PLli0ICQlxnrNp0yZs3boVGRkZyM3NRbdu3ZCcnIwbN244z5k1axbOnTuHrKwsHDp0CCdOnMCiRYukHi4REbmzf8uO6aR4ki8hPfvss4iNjUVmZqbzWFxcnPPrhoYGpKWl4fHHH8d9990HAHjttdcQERGBt956CzNnzsQXX3yBw4cP45NPPsGIESMAAOnp6fjpT3+K5557DtHR0VIPm4iIBO4d091zuJjYSwog+QzMO++8gxEjRuCBBx5AeHg4hg8fjp07dzrvv3jxIkpKSpCUlOQ8ZjabMXr0aOTk5AAAcnJyYLFYnMELACQlJcHPzw+5ubken/fmzZuoqKhw+SAi0jKrrRpWW7X3nsBTx3QhsXfHeMdnW5H3np+oBZIHMP/5z3/w8ssvo1+/fnj//ffxm9/8Bg899BB2794NACgpKQEAREREuHxfRESE876SkhKEh4e73N+lSxeEhoY6z3G3YcMGmM1m50dsLK8KiEi7rLZqJG05jqQtx6UPYuwtBCXixN7aqqazM0Q+InkAU19fjx/96Ed45plnMHz4cCxatAgLFy5ERkaG1E/lYvXq1bDb7c6PoiJeFRBR5+Rb7ei76r32V7/1gcV78lBdW4fq2jpcq6yR5kGFtgJCld6Wcl+Y2EsykzwHJioqCgMHDnQ5duedd+Kvf/0rACAyMhIAUFpaiqioKOc5paWliI+Pd55TVlbm8hi3bt3C1atXnd/vLjAwEIGBgVL9M4g6Trx7g1RNCFzyi5UXwHhFc1V6iRRI8hmYu+++G+fPn3c5VlBQgD59+gBwJPRGRkYiOzvbeX9FRQVyc3ORmJgIAEhMTITNZkNeXp7znCNHjqC+vh6jR4+WeshEHWcrAorPNOYBCPkB3L1BamWJBaLjPQcv5QUMzkkxJJ+BeeSRRzBmzBg888wz+O///m+cPn0aO3bswI4dOwAABoMBy5cvxx/+8Af069cPcXFxeOKJJxAdHY37778fgGPGZvLkyc6lp9raWixduhQzZ87kDiRSDk9VSt13b/AKlrTAU8dqBuckM8kDmJEjR+LgwYNYvXo11q9fj7i4OKSlpWHWrFnOcx577DFUVlZi0aJFsNlsGDt2LA4fPoyuXbs6z9m3bx+WLl2KiRMnws/PDzNmzMDWrVulHi5Rx3mqUirwtHuDVGvvx4VyD8EppFuA759UvLQEOIIXJu+SzLzSSmDatGmYNm1as/cbDAasX78e69evb/ac0NBQ7N+/3xvDI+o8ViklmcRYTNg+JwGL9+S1frKU3FtiMIAhmbEXElF72IqA8vPAG3Mal444lU4+FmMxyT0EItkxgCFqjVB1tKrcNXCZ/VcgbACvREnfygu4Y4lkwQCGqCXiRF3ANXAR3rAZwGhSvtWOVQfOuhyTJf9EqcSJvUISO4MY8iEGMETuxH1exLuKwvrzSlNHxMXr1k4fiEmDIrl0IyYk9hbmOIKYqiv83SCfYgBDJOa+NTrl+z5eYf0dtTFIl0b2DVVU8KKYmSBLLGcgSTaSF7IjUjX2eSEViLGYsDJ5gPP2FalaCRCpCAMYIk86sjWaVUrJh3qKZmGW7MnzblfqtigvYGdq8ikGMESdJU5mZAsB8rGfDomUtqFje4l//reNYhBDPsMcGKLO8lSllMmM5GWDY8wAgHH9bsPfzpbINxAm85JMGMAQScG9SimpnjhRVjFJsyKDY8z4euNUl91SsmEyL8mAS0hERB4Iu462z0lQ1A4kInJgAENE1AIGL0TKxACGiIiIVIcBDFFL7NxRQUSkRAxgiDwRtoae2Mxt0URECsRdSESemHs1bo3mtmhdYnVbImVjAEPUHG6N1h1xNdsle/Jg8jcqcgu1KoibovL3iLyAAQwRERzBS9KW4wCAtJnxqK6tw+75o7gLqSPcm6KmnmYQQ5JjDgwREYBrlTWorq1zKcvfk7MvHeOpKaqtCCg+w1YDJBnOwBARaYBicnbEDU2Fpqj2b4HMKZyRIUlxBoaISMVCugXA5G+UvyN1S01NPc3IEHUSZ2CIBLYi16tHIhWIsZiQMScBc189jWuVNfLl7HhqauoeqJg560LSYQBDBDRNOmTdF1IRIVdnWvpJHFo21tmp2ufcd+5xpoW8iAEMaZewjVOsuS2dwhR3yk6gdyLX53Vu1YGzcg+hw/KtdvkCmOawojV5AQMY0ibxjIpYawmEYf0ZvBBJhRWtyYsYwJA2iWdUwvo7jpUXOJILq64wSCHyBXFejKecGKJOYABD2hbWH4iOl3sURPolzothAEMSYgBD+sQy50REqsYAhvTHU1EtIg/YB4lIuVjIjvSHRbWoDbbPSWAfJCIFYwBD+sWiWtQCBi9EysYlJCIiD7h8JAPmplE7MIAhYvsAcrMyeQBnYHzNvRo2Gz5SK7iERPrVUvM50rWenH3xPeamUTtxBob0y9yrafM5XvERyYu5adRGDGBI39ybzxEByuslRERNcAmJiEhE1m7OemUrYi4atRtnYIiIVE68Y0p1u6fck3eZh0ZtxBkY0h5ezZHOxFhM2D4nwfm11VYNq61a5lG1kbjxauppR24aURtwBoa0pS1Xc/Yi34+LyMuEbd9WWzUeyMgBAHz46Hj1bAcP6+/IR3PffeReG4a1Yuh7DGBIW8RXc70TXd/ghG3TJzZzqpo061plDapr65xfqyaA8cT9gmT2AWBvCmvFEAAuIZFWCVdzYpZYxxveouN84yNSA/faMOUFrBVDTpyBIX3htmnSuGK15L60h3ttGNaKITCAIbUS1sEB17VxJu9SB+Rb7ZiWflLuYUhi65ELcg+hdeLf0+Z+Z/m7TK1gAEPqI14XBzyvjTO/hdoh32qXewj6IG7fISb+nXU/h7/P1AwGMKQ+4kRdwPFGJ6yNe0reJSJlEPLQ3HNXxDuK3M8J6tn4NXcQkggDGFKvsP6ejzF4IVKutuSheTqHOwjJDQMYUgdx7QciaiKkWwBM/kbnFmoAuFJZI+OIJCSelRHPyJCucRs1KZ+Q87JjvOOz/Vu5R0SkODEWEz58dDwemnC789iSPXnqqcjbGkssEB3PGVZyYgBDyudeC4JXXyQxrcxUxFhMmDQoEgCwMnkAqmvrcE0j/zaPyguA4jOOixzSHQYwpB6s/UBeYLVVY/P75+UehmQGx5jx9capGN//NrmH4j3inUrCzCyDGN1hDgxpA3cnUAdYbdUuW6hN/kb1dXPWI3FOTHmBI5ARZmbZJ0k3GMCQurG/EXWQ1VaNpC3HnUmv2+ckYHCMWd29g/TEfaeS/Vsgcwr7JOkIAxhSN/fdCXzDojYSNz0EHPkjDF5UTJwrd2Kz4zbfDzSNAQypj/tyEfsbEZGAuXK6wSReUg8uFxER0fc4A0PqYe7F5SIiIgLAAIbUhstFREQEHywhbdy4EQaDAcuXL3ceu3HjBlJTU9GzZ090794dM2bMQGlpqcv3FRYWYurUqQgKCkJ4eDhWrlyJW7dueXu4REREpAJenYH55JNPsH37dgwdOtTl+COPPIL33nsPf/nLX2A2m7F06VKkpKTgo48+AgDU1dVh6tSpiIyMxKlTp3Dp0iU8+OCD8Pf3xzPPPOPNIZMSCH2PAOa5EBGRR16bgbl+/TpmzZqFnTt3IiQkxHncbrfjlVdewfPPP48JEyYgISEBmZmZOHXqFD7++GMAwAcffIDPP/8ce/fuRXx8PKZMmYKnnnoK27ZtQ02Nhstik2vfI/Y+IqLOsBU5Wg2w3YAmeS2ASU1NxdSpU5GUlORyPC8vD7W1tS7H77jjDvTu3Rs5OTkAgJycHAwZMgQRERHOc5KTk1FRUYFz5855fL6bN2+ioqLC5YNUSKjlkLLT8VFbBVw6I/eoiEht7N82vRhiEKMpXllCev311/Hpp5/ik08+aXJfSUkJAgICYLFYXI5HRESgpKTEeY44eBHuF+7zZMOGDVi3bp0EoydFCOvPbdNE1HHiiyGgsd0ANwFohuQBTFFRER5++GFkZWWha9euUj98s1avXo0VK1Y4b1dUVCA2lj+oqsYqu0TUVs31Qwvr79txkM9IvoSUl5eHsrIy/OhHP0KXLl3QpUsXHD9+HFu3bkWXLl0QERGBmpoa2Gw2l+8rLS1FZKSjDXxkZGSTXUnCbeEcd4GBgQgODnb5IJWxFTkas4lZYoHoeAYvROQZZ2p1S/IZmIkTJ+Ls2bMux+bNm4c77rgDv/3tbxEbGwt/f39kZ2djxowZAIDz58+jsLAQiYmJAIDExEQ8/fTTKCsrQ3h4OAAgKysLwcHBGDhwoNRDJiUQkneFRmx8EyKSxJVKjW98cJ+pFXYwkuZJHsD06NEDgwcPdjnWrVs39OzZ03l8wYIFWLFiBUJDQxEcHIxly5YhMTERd911FwBg0qRJGDhwIObMmYNNmzahpKQEjz/+OFJTUxEYGCj1kEkJxOvVvRM540LUSSHdAmDyN2LJnjx8+Oh4bTeqFBe4ZACjG7L0QnrhhRcwbdo0zJgxA+PGjUNkZCQOHDjgvN9oNOLQoUMwGo1ITEzE7Nmz8eCDD2L9+vVyDJd8Kaw/gxciCcRYTMiYk4Dq2jpc0/osDOmST1oJHDt2zOV2165dsW3bNmzbtq3Z7+nTpw/+9re/eXlkRETa1bNbgNxDUB6hUCY3BqgeeyERke6Z/I0I4R977bN/C2ROacy1Sz3NIEbFZFlCIiJSiu1zErSfI0IOQq7duJWOz8yXUTUGMESkazEWE4MXLWquLgwAmL+fdSkvYHVeFWMAQ74h9CThmwUReVNb6sII5xxYyBYDKsYcGPI+9xovXHcmBdB8fRSRaekncWjZWAyOMcs9FO/zVMHbfanI3MtxTmEOWwyoGGdgyPu47kwKY7VVY8mePF0l7+Zb7XIPwXfaUsHbEss2AyrHGRjyHbPbm4mwnRFo2kKAyIuuVdagurYOu+eP0k3+y6oDZzE4xqyPWZj2Et5/uLVaVRjAkDzEy0oCthAgH9NbnZR8q50BjJg4FwbgErfKMIAheYhbBwjTuLz6ISJfEufLlBcwH0ZlGMCQd7R1eSisv2OtmogkZ7VVyz0E5RP3USJVYQBD0mtteYj5LkQ+wR5IpGUMYEg6wqxLeYHn5SGg6Xozc16IiKgDGMCQNNxnXfyDgN6JTadmhfVmgDkvJBs91YAhkZaq85LqMIAhabgn5TYXnHC9mWSmxxowuteW6ryC8gJeXKkEAxiSFpNySeH0WANG9zxV53Un3lLN7dSqwACGiHRJbzVgdK+12V8hyBHaCxTmNB4nRWIAQ0SkUSxa105CsMKZGFVgLyQiIo0aHGPG1xun4i9LEgEA6979nLVhWiPMxKTsZO82hWMAQ0SkcSP7hmL3/FGorq1jbZi2YKNHVWAAQ0SkA8z5Ia1hAENEumG1VeNC2XW5hyErLiGRVjCAISJdsNqqkbTlOJa/cUaXNWCEwGXxnjwGMaQJ3IVERLog1H9J+0U8RsaF6q4GjDj35Vplje7+/aQ9nIEhIl25Pbw7/3gTaQADGCIiHWBNGNIaBjBERDowOMaMQ8vGyj0MIskwgCEiXWDiKpG2MIAhIs2z2qqxeE+e82siUj/uQiIizXPfgUPUYbailrtak88wgKG2EX5pxfgLTER6YisCto1y9Ehio0fZMYCh1ol/acX4C0wqxN041GFVVxzvg+NWAic2O27z/U82DGCodcIvbcrOxgZn5QWOdvP8BSYVObRsLAMYaj9hBrq8wHHbHNv0Ps5I+xwDGGq7sP5AdLzcoyAi8h37t0DmlMYZaP8gR7Difh9npH2OAQwREVFz3Gegg3o25gNySUlWDGCIiIhaI56BFgIYe5Hjs5lBixxYB4aISGempZ9EvtUu9zDUK6inY8noxGbXJSXyKc7AEBHpUL7VzoTmjrLEOvJdhORd9xIT5BMMYIiIiJojLBO5s8Q25rswgJEFl5CIiIjccZlI8TgDQ56JaxsQEemN+zIRdxcpDgMYasq9XHbKzubPFQo7CZ+JiLRCvExEisMAhpryVNvAnTC9emBh4zFOsxIRkY8wgKHmCbUNPCWxiadXBZxmJSIiH2EAQ81rLYmN06tERCQTBjDUPHMvJrGRquVb7ZiWfhIbU4bIPRTFWXXgLAbHmFkLxhvY4NEnGMBQyzjLQiomVJs98dVlmUeiTCxm5wXumyDY4NFrWAeGXNmKuKOINCOkWwAA4G9nS2QeiTIIr4dg1YGzbCkgpfICoDCncRNEbRWL3HkRZ2CokfuVA3cUkcrFWExyD0FRYiwmbJ+TgMV78pzHOAsjAfddmf5BQFR84/1cUvIKBjB65v5LJW4b3zuRv2hEGsSgzgvcd2WK+yPZvwUyp3BJyQsYwOiVp3VaQVh//oIRaZT7MpL7beog93xBIYDxVFeL76+SYA6MXol/qbhOS6QbMRYTPlo1AWunD3TeJi8S6miZGbRIjQGM3vGXikh3YiwmjOwbKvcwtI3NIL2OS0jkwJ1HpEFXKmucX5v8jVwuId9xbwbJWW7JMYDRO0/Z87xSIA2w2qqxZE8eTP5GvLZgFKItJi6XkG+J82IYwEiOAYzeiavtAtzmR5pxrbIG1bV12D1/FJdLiDSIAYxeCFumBeIlI1bbJQ3ryWUjUhLhvZcXi53GAEYPxFumxbhcRETkG56W61kTplMYwOiBuEBdWP/G47wCICLyDXFSb3mBI5BhTZhOkXwb9YYNGzBy5Ej06NED4eHhuP/++3H+/HmXc27cuIHU1FT07NkT3bt3x4wZM1BaWupyTmFhIaZOnYqgoCCEh4dj5cqVuHXrltTD1Zew/kB0fOMHf3GIiHzHEut47xVfSFKHSR7AHD9+HKmpqfj444+RlZWF2tpaTJo0CZWVlc5zHnnkEbz77rv4y1/+guPHj6O4uBgpKSnO++vq6jB16lTU1NTg1KlT2L17N3bt2oU1a9ZIPVwiIl2bln6SDR2VwFYEFJ9xfKY2kXwJ6fDhwy63d+3ahfDwcOTl5WHcuHGw2+145ZVXsH//fkyYMAEAkJmZiTvvvBMff/wx7rrrLnzwwQf4/PPP8eGHHyIiIgLx8fF46qmn8Nvf/hZPPvkkAgKYlEdEJBU2dJSZp9YunCFvldcr8drtjsg+NNSxjTEvLw+1tbVISkpynnPHHXegd+/eyMnJAQDk5ORgyJAhiIiIcJ6TnJyMiooKnDt3zuPz3Lx5ExUVFS4fRETkmbioHwv8yYytXTrEqwFMfX09li9fjrvvvhuDBw8GAJSUlCAgIAAWi8Xl3IiICJSUlDjPEQcvwv3CfZ5s2LABZrPZ+REby+iViKg5MRYTts9JcH5NCsDWLu3i1QAmNTUV+fn5eP311735NACA1atXw263Oz+KiriOSETUEgYuKsH8GI+8to166dKlOHToEE6cOIFevXo5j0dGRqKmpgY2m81lFqa0tBSRkZHOc06fPu3yeMIuJeEcd4GBgQgMDJT4X6Fi4sJ17HNERC2Yln4Sh5aNZR6MUoiL3QHMj2mG5DMwDQ0NWLp0KQ4ePIgjR44gLi7O5f6EhAT4+/sjOzvbeez8+fMoLCxEYmIiACAxMRFnz55FWVmZ85ysrCwEBwdj4MCBUg9Ze4SEsB3jHR8HFrJoHemK1VYNq61a7mGoCnciycRW5BqwCMXudox3vI9f+oz5Mc2QfAYmNTUV+/fvx9tvv40ePXo4c1bMZjNMJhPMZjMWLFiAFStWIDQ0FMHBwVi2bBkSExNx1113AQAmTZqEgQMHYs6cOdi0aRNKSkrw+OOPIzU1lbMsbeGpcB2L1pFOWG3VSNpyHNW1dXIPRfGYyCsz+7dA5pTG2ZWoYZ6L3QHMj/FA8gDm5ZdfBgDcc889LsczMzPx61//GgDwwgsvwM/PDzNmzMDNmzeRnJyMl156yXmu0WjEoUOH8Jvf/AaJiYno1q0b5s6di/Xr10s9XG0TCtcR6YjQxJFaJyTyLt6Tx3wYOYgvNnsnNl5k8mKzTSQPYBoaGlo9p2vXrti2bRu2bdvW7Dl9+vTB3/72NymHRkREbhi4KEBYfwYtHeD1OjBERETkgZ27ijqDAQwRaRpzO0hxhGTdE5u5waIT2I1aa8QZ7UQ6tzJ5AJdI2uhKZY3cQ9APcWdqbrDoMM7AaImwfZrbpokAAD05+9KqkG4BMPkbsWRPHree+5LQmZrBS4cxgNEScUY7ix0RsTBbG8RYTMiYk4Dq2jpc4yyMOgiVeXVenZdLSFrEjHYiVpZtB2GmymqrRki3AC67KZm4dgyg6+q8nIFRM/bHICIJLd6Th6Qtx7mUpCTuO5XEM+0pO3VdnZczMGpkKwLKzwNvzGms4PiLPUDVVblHRkQqJywlcRZGZs3tVBICGqHKuo4xgFEbIVFXCFxSdgLvPgzsneG4n8m7RETq575TCWga0Oh05kXAAEZtPJWe7p3Y+IPMLXlERNpgiXV9P3ffes0AhlRJnKjr/kNOpGOsZ0Kaxfd6F0ziVRMWqSNqkdVWjSV78mDyN7ICL5HGcQZGLdxzX5jnQtSE0Il69/xRTEIlfbEV6a6yLwMYtWiu7ToRNcEKvKQr4towOqoLwyUkpRJXWiw+07h0xCJ1REQkJlzgjlupq7ownIFRIvFykRiXjoiIqDlmfV3cMoBRIvFykbhYkY7WNonaK99qx7T0k3IPQ5WY8ExqxCUkJQvr7+hWKnwweCFqVr7VLvcQVCvGYsLK5AFyD4M6yr3dgE4wgCEiIiY+q1Fz7QZ0gktIREREauTebkAnybsCBjBERERqJa7Oq7MAhktIRESEwTFm59dsx0BqwACGiIgwOMaMj1ZNgMnfiCV78mC1Vcs9JKIWMYBRCqFwnU2f2eREnSXeCsxtwR0TYzEhY04CqmvrcI2zMKRwzIFRAvc+RxPXyD0iIlXJt9qxeE8eAGD7nAT2QeoE7kbSEI33R+IMjBIIhesmb3TcPrxKl1viiDpKXAOGwQvpXnkBcOFDx4XxjvGOzxqc3ecMjJL0TnTdEqfBiJmIiLxEqAtzYKHjtn+Q48L48CrH3xWN/U1hAKM04i1xRNQmzH8hgmtdGEDztWEYwBCR6nX1NwJg/gtRk4tgDQcwzIEhIlWz2qqxZE8eTP5Gl1omRKRtnIEhIlW7VlmD6to67J4/irMvRDrCGRg5CbVfygvkHgmR6nH7r7SmpZ9kh29SNM7AyEVc+wXgtmkiUgRxErTVVs1lOa0QXyhrZJcrAxi5CLVfUnYCYf018wNFROoWYzFh+5wELN6TxyU5LXDfWg04bqeeVv3fHAYwcgvrD0THyz0KItVizx7pMXDREPet1eUFjmCmMEf1NccYwBCRallt1c4WAlzukB67UmuEeGu1p2J3Kp2NYRKvHGxFTNwlkoC44SCbD0onpFsAu1JrlTAjs+i4I4Whtkq1tWIYwPiakLx7YCETd4lIkdiVWuMssY7UhbD+co+kU7iE5Eu2Ise6o5C82ztRldN2RKR93JZOSscAxlfE26b9gxi8EBGRMpQXqDKZlwGMr4i3TTN4ISIiuYkTelWYzMscGF8QJ+2G9VfVDwgREWmUkNCr0mRezsB4m/vSEZN2iYhIKSyxrjViVLSUxADG27h0RERESua+lPSLPUDYAMX/veISkq9w6YjIq1jEjqiDhKWk2X913N47w7FyYCuSd1ytYABDRKp3aNlYBjBEnWGJBW5PUlVODJeQvMVW5PjPZ8VdIiJSC3FOjMIxgJGarQgoPw+8MccRwQJM3iXyEvbq8T6+xqRUDGCk5L7jaPZfgaAwVWV1E6mF1VaNJXvyYPI3IoRVYyUn9EOa++pp/GVJIkb2DZV7SEQumAMjJfGOo9TTjvXE6HgGL0RecK2yBtW1dciYk4AYi0nu4WhOjMWEtdMHAgAeyMhhU0c9Ki8Ais8oNpmXMzDewB1HRD7Dnj2+ca2yhoGiXoi3VQOKrdLLAIaIiDzizi6dErZVCxtRDix0fK2wAIZLSFIRtwsgItKAwTFmHFo2Vu5hkBwssY4UiLD+co+kWZyBkQLbBRD5HHfHEPmQAtsMMICRAtsFEPkUdyAR+YiC2wxwCUlKTN4l8gnuQCLyEQW3GeAMTEcIVXYBLhcRyYg7kIh8wBLbGMgU5igmqZcBTHuJ810Ax5TaxDXyjomIiMjbFNZmQNFLSNu2bUPfvn3RtWtXjB49GqdPn5Z7SK75LsKU2uFVTN4lIiLyIcXOwLzxxhtYsWIFMjIyMHr0aKSlpSE5ORnnz59HeHi43MNz5LtExzfulVdYdjYREZHXKGBXkmJnYJ5//nksXLgQ8+bNw8CBA5GRkYGgoCC8+uqrcg/NlbBXnsELERFpnXhXkszJvIqcgampqUFeXh5Wr17tPObn54ekpCTk5OR4/J6bN2/i5s2bztt2ux0AUFFRIe3gvrsO3GxwfJb6sYmoTa5/V4H6m1W4/l0FKioMcg9H0/hakws/MzAnG/j2NPDuQ0DpN45jEhL+bjc0NLR4niIDmPLyctTV1SEiIsLleEREBL788kuP37NhwwasW7euyfHYWC/NjGz8sXcel4jaLDFN7hHoB19r8siLfwu/++47mM3NB0eKDGA6YvXq1VixYoXzdn19Pa5evYqePXvCYNDXVUNFRQViY2NRVFSE4OBguYejeXy9fYuvt+/xNfctvb/eDQ0N+O677xAdHd3ieYoMYMLCwmA0GlFaWupyvLS0FJGRkR6/JzAwEIGBgS7HLBaLt4aoCsHBwbr84ZcLX2/f4uvte3zNfUvPr3dLMy8CRSbxBgQEICEhAdnZ2c5j9fX1yM7ORmJioowjIyIiIiVQ5AwMAKxYsQJz587FiBEjMGrUKKSlpaGyshLz5s2Te2hEREQkM8UGML/4xS9w+fJlrFmzBiUlJYiPj8fhw4ebJPZSU4GBgVi7dm2TJTXyDr7evsXX2/f4mvsWX++2MTS0tk+JiIiISGEUmQNDRERE1BIGMERERKQ6DGCIiIhIdRjAEBERkeowgNGwr7/+GgsWLEBcXBxMJhN++MMfYu3ataipqZF7aJr19NNPY8yYMQgKCtJ9IUVv2bZtG/r27YuuXbti9OjROH36tNxD0qwTJ05g+vTpiI6OhsFgwFtvvSX3kDRtw4YNGDlyJHr06IHw8HDcf//9OH/+vNzDUiwGMBr25Zdfor6+Htu3b8e5c+fwwgsvICMjA7/73e/kHppm1dTU4IEHHsBvfvMbuYeiSW+88QZWrFiBtWvX4tNPP8WwYcOQnJyMsrIyuYemSZWVlRg2bBi2bdsm91B04fjx40hNTcXHH3+MrKws1NbWYtKkSaisrJR7aIrEbdQ6s3nzZrz88sv4z3/+I/dQNG3Xrl1Yvnw5bDab3EPRlNGjR2PkyJF48cUXATgqdMfGxmLZsmVYtWqVzKPTNoPBgIMHD+L++++Xeyi6cfnyZYSHh+P48eMYN26c3MNRHM7A6IzdbkdoaKjcwyBqt5qaGuTl5SEpKcl5zM/PD0lJScjJyZFxZETeYbfbAYDv2c1gAKMjFy5cQHp6OhYvXiz3UIjarby8HHV1dU2qcUdERKCkpESmURF5R319PZYvX467774bgwcPlns4isQARoVWrVoFg8HQ4seXX37p8j1WqxWTJ0/GAw88gIULF8o0cnXqyOtNRNQZqampyM/Px+uvvy73UBRLsb2QqHmPPvoofv3rX7d4zg9+8APn18XFxbj33nsxZswY7Nixw8uj0572vt7kHWFhYTAajSgtLXU5XlpaisjISJlGRSS9pUuX4tChQzhx4gR69eol93AUiwGMCt1222247bbb2nSu1WrFvffei4SEBGRmZsLPj5Nu7dWe15u8JyAgAAkJCcjOznYmktbX1yM7OxtLly6Vd3BEEmhoaMCyZctw8OBBHDt2DHFxcXIPSdEYwGiY1WrFPffcgz59+uC5557D5cuXnffxitU7CgsLcfXqVRQWFqKurg5nzpwBANx+++3o3r27vIPTgBUrVmDu3LkYMWIERo0ahbS0NFRWVmLevHlyD02Trl+/jgsXLjhvX7x4EWfOnEFoaCh69+4t48i0KTU1Ffv378fbb7+NHj16OHO7zGYzTCaTzKNToAbSrMzMzAYAHj/IO+bOnevx9T569KjcQ9OM9PT0ht69ezcEBAQ0jBo1quHjjz+We0iadfToUY8/z3PnzpV7aJrU3Pt1Zmam3ENTJNaBISIiItVhQgQRERGpDgMYIiIiUh0GMERERKQ6DGCIiIhIdRjAEBERkeowgCEiIiLVYQBDREREqsMAhoiIiFSHAQwRERGpDgMYIiIiUh0GMERERKQ6DGCIiIhIdf4/mNO9rcDV2doAAAAASUVORK5CYII=", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "make_uniform_series_plot(2)\n", + "n=2\n", + "uniform_series = np.array(\n", + " [sum(random.uniform(-1, 1) for _ in range(n)) * (np.sqrt(6)/ 2) for _ in range(population_size)])\n", + "plt.hist(uniform_series, bins=200, histtype='step', label=f\"sqrt(6)/2 * n={n}\")\n", + "plt.legend()" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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PIzgAvHDpBIAdEHAASPpqjkjJ9ko5oqOoagwgpHGJCoAk79otbCkAINQRcACYutduAYBQRcABgCDAhpyAtQg4QJhxf5BKYp5NgLl/F2zICViPgAOEEc+dwyWxe3gAVTe26rulZV6/i6XXjNKyjQfU0NJOwAH6iIADhBH3zuHFs7IlSUXrKyg4FyCev4us5IFsyAlYjIADhKEsis0FjazkgRqdniiJDTkBK1EHBwAA2A4BBwAA2A4BBwAA2A4BBwAA2A4BBwAA2A4BBwAA2A4BBwAA2A4BBwACoLqxNdBNAGyNgAMA/WhwfIwc0VEq2V4pR3QU+4EBfkIlYyBMVDe2qrKuOdDNCHvpToe23j6JncMBPyPgAGHAc5NN96gB2wIETrrTccpgU1nXTPgB+oiAA4QBz40dx2cmKd3pMAMOc0GCh/vyVdH6Cjmio7T19kmEHKCXmIMDhJGs5IHmByZzQYKP+/JV8axstXZ0MsoG9IHPAWfnzp269tprlZaWpoiICG3YsMHrccMwtHTpUg0dOlQOh0O5ubn6+OOPvc6pr69Xfn6+EhIS5HQ6NW/ePDU3e88N+MMf/qDLLrtMcXFxysjI0IoVK3zvHYCTcn+YblxwKSMFQSTd6WC3d8ACPgeclpYWXXjhhVq9enWPj69YsUKrVq1SaWmpdu/erfj4eOXl5eno0aPmOfn5+dq/f7+2bNmijRs3aufOnZo/f775uMvl0lVXXaXhw4ervLxcjz32mO677z4999xzvegigJNJdzo0Oj2RcAPAdnyegzN16lRNnTq1x8cMw1BxcbHuuecezZgxQ5L0yiuvKCUlRRs2bNDs2bN18OBBbdq0SXv37tW4ceMkSSUlJZo2bZpWrlyptLQ0rV27Vu3t7VqzZo1iYmJ0/vnnq6KiQk888YRXEAIAAOiJpXNwqqqqVFNTo9zcXPNYYmKiJk6cqLKyMklSWVmZnE6nGW4kKTc3V5GRkdq9e7d5zuWXX66YmK/mBOTl5enQoUNqaGjo8bXb2trkcrm8bgAAIDxZGnBqamokSSkpKV7HU1JSzMdqamqUnJzs9fiAAQOUlJTkdU5PP8PzNbpbvny5EhMTzVtGRkbfOwQAAEKSbVZRLV68WE1NTebtyJEjgW4SAAAIEEsDTmpqqiSptrbW63htba35WGpqqurq6rweP3bsmOrr673O6elneL5Gd7GxsUpISPC6AQCA8GRpwMnMzFRqaqq2bdtmHnO5XNq9e7dycnIkSTk5OWpsbFR5ebl5zvbt29XV1aWJEyea5+zcuVMdHR3mOVu2bNGIESM0ePBgK5sM2FJ1Y6v2VTdpX3UThfwAhCWfV1E1NzersrLSvF9VVaWKigolJSVp2LBhKioq0oMPPqhzzz1XmZmZWrJkidLS0nTddddJkkaOHKmrr75aN998s0pLS9XR0aHCwkLNnj1baWlpkqQbbrhB999/v+bNm6dFixZp3759euqpp/Tkk09a02vAxjy3ZZAkR3SU7sgbEeBWAUD/8jngvPfee7ryyivN+wsXLpQkzZ07Vy+99JLuvPNOtbS0aP78+WpsbNSll16qTZs2KS4uznzO2rVrVVhYqClTpigyMlIzZ87UqlWrzMcTExO1efNmFRQUaOzYsTrrrLO0dOlSlogDZ8BzW4bB8TG65dVyLdt4gGrFAMJKhGEYRqAb4Q8ul0uJiYlqampiPg7Cyr7qJl1TsksbF1yq0emJqm5sZefqEOP+HXruHQaEC6s+v9lsE7C50+1cjeDTfdPN0jljNSQ+hpAK+ICAAwBBxr1PWGVds255tVxz1+yRJHYYB3xAwAGAIOQeedt6+yQ1tLSrsq5ZResr1NDSTsABzgABB7CR6sZWVdY1B7oZsBCXGIHeIeAANuG5PJwVUwDCHQEHsAnP5eGsvAEQ7myzFxWA47KSBxJuAIQ9Ag4AALAdAg4AALAdAg4AALAdAg4AALAdAg4AhJDKumZVN7YGuhlA0CPgAEAI8NyfKvfxHYQc4DQIOAAQAtzbNhTPylZrR6caWtoD3SQgqFHoDwBCRLrToYbkgYFuBhASGMEBAAC2Q8ABAAC2wyUqwAbYRTw8VTe2qqGlXYPjY9ieA+iGgAOEOHYRD0/Vja36bmmZ+XvfevskQg7ggUtUQIjz3EWcD7nwsa+6Sa0dnVowOYtVVUAPCDiATbCLeHhw18Mp2V4pR3SURqcnBrpJQFDiEhUAhBB3PRz33BtGboCeEXAAIMSkOx3maB0BB+gZl6gAAIDtEHAAAIDtEHAAAIDtEHAAAIDtEHAAAIDtEHAAAIDtEHAAAIDtUAcHCGFssgk39/8HbLwJHEfAAUIUm2xC+mrrhqL1FZLExpvA3xFwgBDlucnm+MwkPtDClOfWDZV1zSpaX6GGlnb+f0DYI+AAIY5NNuG5dQOA45hkDAAAbIeAAwAAbIeAAwAAbMfygNPZ2aklS5YoMzNTDodD55xzjh544AEZhmGeYxiGli5dqqFDh8rhcCg3N1cff/yx18+pr69Xfn6+EhIS5HQ6NW/ePDU3sxwWAACcnuUB59FHH9Wzzz6rp59+WgcPHtSjjz6qFStWqKSkxDxnxYoVWrVqlUpLS7V7927Fx8crLy9PR48eNc/Jz8/X/v37tWXLFm3cuFE7d+7U/PnzrW4uAACwIctXUb3zzjuaMWOGpk+fLkn6xje+oZ///Ofas2ePpOOjN8XFxbrnnns0Y8YMSdIrr7yilJQUbdiwQbNnz9bBgwe1adMm7d27V+PGjZMklZSUaNq0aVq5cqXS0tKsbjYAALARy0dwLr74Ym3btk0fffSRJOl///d/tWvXLk2dOlWSVFVVpZqaGuXm5prPSUxM1MSJE1VWViZJKisrk9PpNMONJOXm5ioyMlK7d+/u8XXb2trkcrm8bgAAIDxZPoJz1113yeVy6bzzzlNUVJQ6Ozv10EMPKT8/X5JUU1MjSUpJSfF6XkpKivlYTU2NkpOTvRs6YICSkpLMc7pbvny57r//fqu7AwSd6sZWs6gbAKBnlgec//zP/9TatWv12muv6fzzz1dFRYWKioqUlpamuXPnWv1ypsWLF2vhwoXmfZfLpYyMDL+9HhAIntszSGKLBpyUOwizNxXCleUB54477tBdd92l2bNnS5LGjBmjP//5z1q+fLnmzp2r1NRUSVJtba2GDh1qPq+2tlbZ2dmSpNTUVNXV1Xn93GPHjqm+vt58fnexsbGKjY21ujtAUPHcniEreSAfXuhRdWOrvltaZu5Txt5UCEeWz8H58ssvFRnp/WOjoqLU1dUlScrMzFRqaqq2bdtmPu5yubR7927l5ORIknJyctTY2Kjy8nLznO3bt6urq0sTJ060uslAyMlKHqjR6Yl8aKFH7iC8YHKWWjs61dDSHugmAf3O8hGca6+9Vg899JCGDRum888/Xx988IGeeOIJ3XTTTZKkiIgIFRUV6cEHH9S5556rzMxMLVmyRGlpabruuuskSSNHjtTVV1+tm2++WaWlpero6FBhYaFmz57NCioAOEMEYIQzywNOSUmJlixZoh/96Eeqq6tTWlqa/u3f/k1Lly41z7nzzjvV0tKi+fPnq7GxUZdeeqk2bdqkuLg485y1a9eqsLBQU6ZMUWRkpGbOnKlVq1ZZ3VwgZFQ3tjKxGADOkOUBZ9CgQSouLlZxcfFJz4mIiNCyZcu0bNmyk56TlJSk1157zermASHJc3IxE4sB4PQsDzgArOc5uXh8ZhKXHnBK1Y2tgW4CEHBstgmEkKzkgYQbnNTg+Bg5oqNUsr2SkT6EPUZwgCDH3BucqXSnQ1tvn2TWv2H1FMIZAQcIYsy9ga/SnQ5zlI+Ag3BGwAGCGHNvAKB3mIMDhADm3gCAbwg4AADAdrhEBQA2556kzt5lCCcEHACwKfey8aL1FZLExpsIKwQcALApz2XjlXXNKlpfoYaWdgIOwgIBBwBszHPZOBBOmGQMAABsh4ADAABsh4ADAABsh4ADBCn2oAKA3mOSMRCE2IMKAPqGgAMEIfaggr9U1jVT8A9hgUtUQBBjDypYxbPoX+7jO1Td2BroJgF+RcABgDDgLvpXPCtbrR2damhpD3STAL/iEhUAhIl0p0MNyQMD3QygXzCCAwAAbIeAAwAAbIeAAwAAbIc5OEAQqW5sNXd+BgD0HgEHCBKexf0kUeAPAPqAgAMECc/iflnJAynGBgB9QMABgkxW8kCNTk8MdDMAIKQxyRgAANgOAQcIAuwcDgDW4hIVEEDuYHPLq+XsHA4AFiLgAAHiuWrKER2ll2+awOaaAGARAg4QIJ6rpsZnJhFs0K88L4myYg92RMABAoxRG/SnwfExckRHqWh9hXnMER2lrbdP4v9D2AoBBwDCSLrToa23T1JDS7uk4yM5Resr1NDSTsCBrRBwACDMpDsdpw0z7m1DuHyFUEXAAQB46T4BnstXCEXUwQEAeHFPgF8wOUutHZ3m5SwglPgl4FRXV+v73/++hgwZIofDoTFjxui9994zHzcMQ0uXLtXQoUPlcDiUm5urjz/+2Otn1NfXKz8/XwkJCXI6nZo3b56amymEBgD+UFnXrH3VTapubDWPMWqDUGZ5wGloaNAll1yi6Oho/fa3v9WBAwf0+OOPa/DgweY5K1as0KpVq1RaWqrdu3crPj5eeXl5Onr0qHlOfn6+9u/fry1btmjjxo3auXOn5s+fb3VzASCsea6quqZkl3If3+EVcoBQZfkcnEcffVQZGRl68cUXzWOZmZnmfxuGoeLiYt1zzz2aMWOGJOmVV15RSkqKNmzYoNmzZ+vgwYPatGmT9u7dq3HjxkmSSkpKNG3aNK1cuVJpaWlWNxsAwpLnqirPFVVAqLN8BOdXv/qVxo0bp+9+97tKTk7WRRddpOeff958vKqqSjU1NcrNzTWPJSYmauLEiSorK5MklZWVyel0muFGknJzcxUZGandu3f3+LptbW1yuVxeNwDA6aU7HRqdnqis5IGSxAgObMHygPPpp5/q2Wef1bnnnqu33npLt956q3784x/r5ZdfliTV1NRIklJSUryel5KSYj5WU1Oj5ORkr8cHDBigpKQk85zuli9frsTERPOWkZFhddcAwNbcl6tKtleyLxpCnuWXqLq6ujRu3Dg9/PDDkqSLLrpI+/btU2lpqebOnWv1y5kWL16shQsXmvddLhchBwB84Hm5anB8DJeqENIsDzhDhw7VqFGjvI6NHDlSv/zlLyVJqampkqTa2loNHTrUPKe2tlbZ2dnmOXV1dV4/49ixY6qvrzef311sbKxiY2Ot6gZgOXfhNEl8M0bQ8iwCSMBBKLM84FxyySU6dOiQ17GPPvpIw4cPl3R8wnFqaqq2bdtmBhqXy6Xdu3fr1ltvlSTl5OSosbFR5eXlGjt2rCRp+/bt6urq0sSJE61uMuB3noXTpON7/xTPzg5sowDAxiwPOLfddpsuvvhiPfzww/re976nPXv26LnnntNzzz0nSYqIiFBRUZEefPBBnXvuucrMzNSSJUuUlpam6667TtLxEZ+rr75aN998s0pLS9XR0aHCwkLNnj2bFVQISZ47h0tS0foK7atuCmyjAMDGLA8448eP1xtvvKHFixdr2bJlyszMVHFxsfLz881z7rzzTrW0tGj+/PlqbGzUpZdeqk2bNikuLs48Z+3atSosLNSUKVMUGRmpmTNnatWqVVY3F+hXWckDmcgJAP0gwjAMI9CN8AeXy6XExEQ1NTUpISEh0M1BmNtX3aRrSnZp44JLNTo9kY0MERK6/38L9AerPr/ZbBMIgDPZzRkA0HtstgkAAGyHgAMAAGyHgAMAAGyHgAMAAGyHgAMAAGyHgAP4WXVjqyrrmgPdDAAIKywTB/zIc4sGivohVFXWNVOzCSGHgAP4kecWDeMzk/iAQEhxV90uWl8hR3SUtt4+if+HETK4RAX0g6zkgXwwIOSkOx3aevskFc/KVmtHJ7uLI6QwggP4CXNvYAfpTocakgcGuhmAzwg4gB8w9wYAAouAA/gBc28AILCYgwNYzPPSFHNvACAwGMEBLMSlKQAIDgQcwEJcmgKA4MAlKsAPuDQFAIFFwAEAALZDwAEAALbDHBwAwBlxrw5kXyqEAgIOAOCUPPekkmTuSyUdn1hP4EEwIuAAAE7JvSdVQ0u7KuuaVbS+Qvuqm1S0rsIsicBGnAg2zMEBAJxWutOh0emJyvr7vlTukggLJmexESeCEgEHANBrjNogWBFwAACA7RBwAACA7RBwAACA7bCKCuiD6sZWr8mV7johAIDAIuAAveS5c7gndhFHOKhubA10E4BTIuAAveS5c7h76axElVfYm7voX8n2SsI8ghoBB+ijrOSBGp2eGOhmAP3Cs+jf4PgY6t8gaBFwAAA+SXc6zFFKAg6CFauoAACA7RBwAAB9VlnXzMRjBBUCDtAL1Y2tLAkH5L3TeO7jOwg5CBrMwQF85Lk8nFUkCHfuScd7q+pVtL5CDS3trCJEUCDgAD7yXB4+PjOJN3OEvXSnQw0epRKAYOD3S1SPPPKIIiIiVFRUZB47evSoCgoKNGTIEA0cOFAzZ85UbW2t1/MOHz6s6dOn62tf+5qSk5N1xx136NixY/5uLnDGspIHEm4AIEj5NeDs3btXP/vZz3TBBRd4Hb/tttv061//Wr/4xS+0Y8cOffbZZ7r++uvNxzs7OzV9+nS1t7frnXfe0csvv6yXXnpJS5cu9WdzAQCATfgt4DQ3Nys/P1/PP/+8Bg8ebB5vamrSCy+8oCeeeEKTJ0/W2LFj9eKLL+qdd97Ru+++K0navHmzDhw4oP/4j/9Qdna2pk6dqgceeECrV69Wezs1FwAAwKn5LeAUFBRo+vTpys3N9TpeXl6ujo4Or+PnnXeehg0bprKyMklSWVmZxowZo5SUFPOcvLw8uVwu7d+/v8fXa2trk8vl8roBAIDw5JdJxuvWrdP777+vvXv3nvBYTU2NYmJi5HQ6vY6npKSopqbGPMcz3Lgfdz/Wk+XLl+v++++3oPUAgL6qbmw1t3NgrhoCwfKAc+TIEf3kJz/Rli1bFBcXZ/WPP6nFixdr4cKF5n2Xy6WMjIx+e30AwHHdSylsvX0SIQf9zvJLVOXl5aqrq9M//uM/asCAARowYIB27NihVatWacCAAUpJSVF7e7saGxu9nldbW6vU1FRJUmpq6gmrqtz33ed0Fxsbq4SEBK8bYDUK/AGnVlnXrL1V9Wrt6NSCyVlq7ehkvyoEhOUjOFOmTNGHH37odezGG2/Ueeedp0WLFikjI0PR0dHatm2bZs6cKUk6dOiQDh8+rJycHElSTk6OHnroIdXV1Sk5OVmStGXLFiUkJGjUqFFWNxk4IxT4A07Os6KxJDmiozQ6PTGwjUJYszzgDBo0SKNHj/Y6Fh8fryFDhpjH582bp4ULFyopKUkJCQlasGCBcnJy9K1vfUuSdNVVV2nUqFGaM2eOVqxYoZqaGt1zzz0qKChQbGys1U0GzggF/oCTc1c0do/WDI6PYeQGARWQSsZPPvmkIiMjNXPmTLW1tSkvL0/PPPOM+XhUVJQ2btyoW2+9VTk5OYqPj9fcuXO1bNmyQDQX8EKBP6Bn6U6H198GAQeB1C8B5+233/a6HxcXp9WrV2v16tUnfc7w4cP15ptv+rllwOm5V4Mw9wYAQgd7UQGn4DnvRhJzbwAgRBBwgFPwnHeTlTyQmh5AL1TWNfO3g35HwAHOQFbyQFaEAD7yXFlFPRz0N7/vJg6EKmreAH3jXllVPCubejjod4zgAD2g5g1gjXSnQw3JAwPdDIQhAg7QA2reAEBo4xIVcArUvAGA0ETAAQAAtsMlKgBAv3EXzpTE0nH4FQEHANAvqhtb9d3SMq/CmSwdh78QcIC/c3+zZMUU4B/7qpvMyfuSVLS+Qg0t7QQc+AUBB9CJy8KLZ2cHukmAbbgL/pVsr5QjOkrjM5OoiQO/I+AA+mpZ+ILJWSrZXsmbL2Ahd8E/9whputPB3xj8joADeGCoHPCPdKeDvy/0K5aJAwAA2yHgAD2obmwNdBMAAH1AwAE8dJ8MyYoqAAhNzMEBPPQ0GRIAEHoIOAhLnjVvuocYJkMCQOgj4CDsdK95s/X2SYFuEgDAYszBQdjxrHnT2tFJPQ4AsCFGcBC23JehKuuaA9wSIHx5/v0x7w1WIuAgbLlXTBWtr5AkVk0B/aj735/E5puwFgEHYctzxZTEt0egP3X/+6usa2bzTViKgIOwxoopIHD4+4M/MckYAADYDiM4AICg4q5TJXHpGL1HwAEABI3qxlZ9t7RMrR2dkph4jN4j4MC2+BYIhB53nariWdmSxMRj9BoBB7bkWa1Y4lsgECqqG1slSVnJAwPcEoQ6JhnDljy/BRbPyqZiMRDk3HVxSrZXUpMKlmAEB7bGt0AgNHjWxXFfUvaskcNlZviKgIOwUt3YytYMQJDqXhfHs9oxl5nhKwIOwobn6gyGwIHg5x7V2VtVz2Rj+IyAg7DhOS9nfGYSb5RACEh3OtTApWb0ApOMEXaykgcSbgDA5gg4AADAdiwPOMuXL9f48eM1aNAgJScn67rrrtOhQ4e8zjl69KgKCgo0ZMgQDRw4UDNnzlRtba3XOYcPH9b06dP1ta99TcnJybrjjjt07Ngxq5uLMOKurwEAsD/LA86OHTtUUFCgd999V1u2bFFHR4euuuoqtbS0mOfcdttt+vWvf61f/OIX2rFjhz777DNdf/315uOdnZ2aPn262tvb9c477+jll1/WSy+9pKVLl1rdXIQB6msA9lBZ18wXFZyxCMMwDH++wOeff67k5GTt2LFDl19+uZqamnT22Wfrtdde03e+8x1J0h//+EeNHDlSZWVl+ta3vqXf/va3uuaaa/TZZ58pJSVFklRaWqpFixbp888/V0zM6T+gXC6XEhMT1dTUpISEBH92EUHCvTXD4PgYNbS065qSXdq44FKNTk/0eoz5N0Bo8axMznJx+7Pq89vvc3CampokSUlJSZKk8vJydXR0KDc31zznvPPO07Bhw1RWViZJKisr05gxY8xwI0l5eXlyuVzav39/j6/T1tYml8vldUP4cL8BXlOyS7mP7zjhW16606HR6Ym8KQIhyL1cnKrk8IVfA05XV5eKiop0ySWXaPTo0ZKkmpoaxcTEyOl0ep2bkpKimpoa8xzPcON+3P1YT5YvX67ExETzlpGRYXFvEMzcS8AXTM7iDRCwoXSng8rk8IlfA05BQYH27dundevW+fNlJEmLFy9WU1OTeTty5IjfXxPBhxEawP6Yi4Mz4beAU1hYqI0bN+p3v/udvv71r5vHU1NT1d7ersbGRq/za2trlZqaap7TfVWV+777nO5iY2OVkJDgdQMA2Ifn1g09XYoGPFkecAzDUGFhod544w1t375dmZmZXo+PHTtW0dHR2rZtm3ns0KFDOnz4sHJyciRJOTk5+vDDD1VXV2ees2XLFiUkJGjUqFFWNxkAEAKYiwNfWL5VQ0FBgV577TX993//twYNGmTOmUlMTJTD4VBiYqLmzZunhQsXKikpSQkJCVqwYIFycnL0rW99S5J01VVXadSoUZozZ45WrFihmpoa3XPPPSooKFBsbKzVTYYN8c0OsCe2bsCZsjzgPPvss5KkK664wuv4iy++qB/+8IeSpCeffFKRkZGaOXOm2tralJeXp2eeecY8NyoqShs3btStt96qnJwcxcfHa+7cuVq2bJnVzYXNUPMGACD5IeCcSVmduLg4rV69WqtXrz7pOcOHD9ebb75pZdNgA+56Nt1V1jVL+moIm5o3gP25/+75W0dP2E0cIcOz2FdP3CM26U4Hb3aAjXlONpaO/+2XzhnLRrrwQsBByHDXuimeld1jPQy+xQHhwXOk9m8t7brl1XLNXbOHKsfwQsBByMlKHqjR6YmBbgaAAPIcqd16+yTtrapX0foKNbS0E3AgqR+2agAAwJ88qxxTBBBuBBwAQMijCCC6I+AAAEIeRQDRHXNwAAC2QBFAeCLgAABsx10jx41VluGHgAMAsI3uNXLcqJUTfgg4CGqelYu7fyMDgO48a+S4USsnPBFwELR6qlzM/lIATqenaubUygk/BBwErZ4qF3MdHUBvMAE5/BBwEPSoXAwA8BUBB0HDPd+GURoA/cVznh/vPfZCwEFQ8Jxv417tQKEuAP7UfZ4fE5DthUrGCLjqxlbtrapXa0enll4zSpI0d80eFa2vYFIxAL/xnOdHBWT7YQQH/ar7cLAkr5GbvNGpyhudypAxAL+prGv2+uKUxeRjWyLgoN/0NBxcPDvb/AY1PjPJDDOEGgBW8ywC6IiO0h15IwLdJPgRl6jQb041HEx1UQD+5i4C+PJNEyRJyzYe4DK4jTGCg37HcDCAQHEXAXRXO3ZfBmfujf0QcAAAYaenasfSV/NzGFEOfVyiQkBVN7YGugkA4DU/J/fxHbw32QABBwHhfjMp2V7JNXAAAee+bHWmy8WrG1u1r7qJIBTEuESFflHd2Oq1G3hP18ABIJA896s61aWq7oVJKQ4YnAg48AvPbRck71o37mMnuwYOAIHSfSl56ZyxJ6zydK8IXTA5SyXbK9mdPEgRcGC57t9uTlbrBgCCjXt0ubKuWbe8Wq65a/acdJSG97Lgxhwc9Fn3a9Ge326odQMg1KQ7HZr0D2d7zcnZW1XPnJsQwwgO+qSna9Fu7jDDGwKAUJTudEiZSeYlK0lUQA4hBBz0Sfdr0Xur6s3HWCkFINR5Loj4W0u7bnm1nArIIYKAg17zXBk1Oj3xhG85o9MTWSkFIOR5LojwfE/zXErefSNh3u8Cj4CDXul+acozzEjef+D8oQOwC8+w436/21NVr8feOuS1kTBLxwOPgINT8lzu7TmnZm9VPbuAAwhr7svw7ktWL980QQ0t7SpaX8HS8SBAwMFJdR+lKZ0zVpJ0y6vl5jGWfQMIVz0VLN1X3WQ+3tMXRPQfAg68eF5HrqxrVmtHp5ZeM0qPvXVIc9fskSTzmwrLvgGEu5MVLPW8bOW5wrT7FhCEH/8h4MDkOWLj5oiOUt7oVOWNTmUCHQCcRvfLVkuvGaVlGw/orX01XvN03Jiv4z8EnDDUfdjUfd89YlM8K1tZf9+PhcnCAHDmul+2kqTH3jrkNU9nyN+PV9Y1q2h9hfZW1Zt7YPEF0joEnDDTfV7N8uvHaPHrH3rN/mdeDQD0XvfLVicrl+G575Wb54gOc3j6JqgDzurVq/XYY4+ppqZGF154oUpKSjRhwoRANyvonEn9he6jNO55Ne4N5dzfKvhDAgBrnWyejudoj/TViI77PjuW903QBpz169dr4cKFKi0t1cSJE1VcXKy8vDwdOnRIycnJgW5evzldeOk+b8a92mmIR4VNd/VNz3M859UQagAgMHoKP+4Cqt2rxLsvY3nqPtWA9/OvRBiGYQS6ET2ZOHGixo8fr6efflqS1NXVpYyMDC1YsEB33XXXaZ/vcrmUmJiopqYmJSQk+Lu5feYZZCSZ1257Ci+eq5f2VTfpmpJdKp6VrcHxMV5BxpNn8OEPAACCT09fWF+ZN0E/eGFPj+/r7nM8pxr0dInLLVTe+636/A7KEZz29naVl5dr8eLF5rHIyEjl5uaqrKysx+e0tbWpra3NvN/UdLwWgcvlsrx9n7uO6vPmttOfeIbqv+xQ0boPdLSjyzwWFx2pn0w5Vy3NX+iR68fIGR+jonUfaM6zbysuOlLFsy9S0tei9ennLepq+1Kpji6NSo3VGzdfpMYv2094DefXYpTmjP37vQ65XB2WtR8A0HeDIuX1Hn78fXvASd/X3Z8dP37lHcVFR+qOKefq0U2HtOPDP5ufGd0/V9yfHVY4e2Cszk6Is+RneXJ/bvd5/MUIQtXV1YYk45133vE6fscddxgTJkzo8Tn33nuvIYkbN27cuHHjZoPbkSNH+pQlgnIEpzcWL16shQsXmve7urpUX1+vIUOGKCIiosfnuFwuZWRk6MiRIyFxGauvwq2/Uvj1Odz6K4Vfn8Otv1L49Tnc+it593nQoEH64osvlJaW1qefGZQB56yzzlJUVJRqa2u9jtfW1io1NbXH58TGxio2NtbrmNPpPKPXS0hICJv/iaTw668Ufn0Ot/5K4dfncOuvFH59Drf+Sl/1OTExsc8/K9KC9lguJiZGY8eO1bZt28xjXV1d2rZtm3JycgLYMgAAEAqCcgRHkhYuXKi5c+dq3LhxmjBhgoqLi9XS0qIbb7wx0E0DAABBLmgDzqxZs/T5559r6dKlqqmpUXZ2tjZt2qSUlBTLXiM2Nlb33nvvCZe27Crc+iuFX5/Drb9S+PU53PorhV+fw62/kn/6HLR1cAAAAHorKOfgAAAA9AUBBwAA2A4BBwAA2A4BBwAA2I7tA87q1av1jW98Q3FxcZo4caL27Nlz0nP379+vmTNn6hvf+IYiIiJUXFzcfw21iC/9ff7553XZZZdp8ODBGjx4sHJzc095frDypc+vv/66xo0bJ6fTqfj4eGVnZ+vVV1/tx9b2nS/99bRu3TpFRETouuuu828D/cCXPr/00kuKiIjwusXFWb9fjj/5+jtubGxUQUGBhg4dqtjYWP3DP/yD3nzzzX5qrTV86fMVV1xxwu84IiJC06dP78cW942vv+Pi4mKNGDFCDodDGRkZuu2223T06NF+am3f+dLfjo4OLVu2TOecc47i4uJ04YUXatOmTb6/aJ82eghy69atM2JiYow1a9YY+/fvN26++WbD6XQatbW1PZ6/Z88e46c//anx85//3EhNTTWefPLJ/m1wH/na3xtuuMFYvXq18cEHHxgHDx40fvjDHxqJiYnG//3f//Vzy3vP1z7/7ne/M15//XXjwIEDRmVlpVFcXGxERUUZmzZt6ueW946v/XWrqqoy0tPTjcsuu8yYMWNG/zTWIr72+cUXXzQSEhKMv/zlL+atpqamn1vde772t62tzRg3bpwxbdo0Y9euXUZVVZXx9ttvGxUVFf3c8t7ztc9/+9vfvH6/+/btM6KioowXX3yxfxveS772d+3atUZsbKyxdu1ao6qqynjrrbeMoUOHGrfddls/t7x3fO3vnXfeaaSlpRm/+c1vjE8++cR45plnjLi4OOP999/36XVtHXAmTJhgFBQUmPc7OzuNtLQ0Y/ny5ad97vDhw0Mu4PSlv4ZhGMeOHTMGDRpkvPzyy/5qouX62mfDMIyLLrrIuOeee/zRPMv1pr/Hjh0zLr74YuPf//3fjblz54ZcwPG1zy+++KKRmJjYT62znq/9ffbZZ41vfvObRnt7e3810XJ9/Tt+8sknjUGDBhnNzc3+aqKlfO1vQUGBMXnyZK9jCxcuNC655BK/ttMqvvZ36NChxtNPP+117Prrrzfy8/N9el3bXqJqb29XeXm5cnNzzWORkZHKzc1VWVlZAFvmH1b098svv1RHR4eSkpL81UxL9bXPhmFo27ZtOnTokC6//HJ/NtUSve3vsmXLlJycrHnz5vVHMy3V2z43Nzdr+PDhysjI0IwZM7R///7+aG6f9aa/v/rVr5STk6OCggKlpKRo9OjRevjhh9XZ2dlfze4TK967XnjhBc2ePVvx8fH+aqZletPfiy++WOXl5eZlnU8//VRvvvmmpk2b1i9t7ove9Letre2Ey8oOh0O7du3y6bWDtpJxX/31r39VZ2fnCZWPU1JS9Mc//jFArfIfK/q7aNEipaWlef2PGMx62+empialp6erra1NUVFReuaZZ/RP//RP/m5un/Wmv7t27dILL7ygioqKfmih9XrT5xEjRmjNmjW64IIL1NTUpJUrV+riiy/W/v379fWvf70/mt1rvenvp59+qu3btys/P19vvvmmKisr9aMf/UgdHR269957+6PZfdLX9649e/Zo3759euGFF/zVREv1pr833HCD/vrXv+rSSy+VYRg6duyYbrnlFv2///f/+qPJfdKb/ubl5emJJ57Q5ZdfrnPOOUfbtm3T66+/7nNot+0IDnzzyCOPaN26dXrjjTdCbkKmrwYNGqSKigrt3btXDz30kBYuXKi333470M2y3BdffKE5c+bo+eef11lnnRXo5vSbnJwc/eAHP1B2drYmTZqk119/XWeffbZ+9rOfBbppftHV1aXk5GQ999xzGjt2rGbNmqW7775bpaWlgW5av3jhhRc0ZswYTZgwIdBN8Zu3335bDz/8sJ555hm9//77ev311/Wb3/xGDzzwQKCb5hdPPfWUzj33XJ133nmKiYlRYWGhbrzxRkVG+hZZbDuCc9ZZZykqKkq1tbVex2tra5WamhqgVvlPX/q7cuVKPfLII9q6dasuuOACfzbTUr3tc2RkpLKysiRJ2dnZOnjwoJYvX64rrrjCn83tM1/7+8knn+hPf/qTrr32WvNYV1eXJGnAgAE6dOiQzjnnHP82uo+s+DuOjo7WRRddpMrKSn800VK96e/QoUMVHR2tqKgo89jIkSNVU1Oj9vZ2xcTE+LXNfdWX33FLS4vWrVunZcuW+bOJlupNf5csWaI5c+boX//1XyVJY8aMUUtLi+bPn6+7777b5w/+/tSb/p599tnasGGDjh49qr/97W9KS0vTXXfdpW9+85s+vXbw/qv0UUxMjMaOHatt27aZx7q6urRt2zbl5OQEsGX+0dv+rlixQg888IA2bdqkcePG9UdTLWPV77irq0ttbW3+aKKlfO3veeedpw8//FAVFRXm7dvf/rauvPJKVVRUKCMjoz+b3ytW/I47Ozv14YcfaujQof5qpmV6099LLrlElZWVZniVpI8++khDhw4N+nAj9e13/Itf/EJtbW36/ve/7+9mWqY3/f3yyy9PCDHuQGsE+XaSffn9xsXFKT09XceOHdMvf/lLzZgxw7cX93EydEhZt26dERsba7z00kvGgQMHjPnz5xtOp9NcMjpnzhzjrrvuMs9va2szPvjgA+ODDz4whg4davz0pz81PvjgA+Pjjz8OVBd84mt/H3nkESMmJsb4r//6L68ll1988UWguuAzX/v88MMPG5s3bzY++eQT48CBA8bKlSuNAQMGGM8//3yguuATX/vbXSiuovK1z/fff7/x1ltvGZ988olRXl5uzJ4924iLizP2798fqC74xNf+Hj582Bg0aJBRWFhoHDp0yNi4caORnJxsPPjgg4Hqgs96+//1pZdeasyaNau/m9tnvvb33nvvNQYNGmT8/Oc/Nz799FNj8+bNxjnnnGN873vfC1QXfOJrf999913jl7/8pfHJJ58YO3fuNCZPnmxkZmYaDQ0NPr2urQOOYRhGSUmJMWzYMCMmJsaYMGGC8e6775qPTZo0yZg7d655v6qqypB0wm3SpEn93/Be8qW/w4cP77G/9957b/83vA986fPdd99tZGVlGXFxccbgwYONnJwcY926dQFode/50t/uQjHgGIZvfS4qKjLPTUlJMaZNm+Zz/YxA8/V3/M477xgTJ040YmNjjW9+85vGQw89ZBw7dqyfW903vvb5j3/8oyHJ2Lx5cz+31Bq+9Lejo8O47777jHPOOceIi4szMjIyjB/96Ec+f+AHki/9ffvtt42RI0casbGxxpAhQ4w5c+YY1dXVPr9mhGEE+fgWAACAj2w7BwcAAIQvAg4AALAdAg4AALAdAg4AALAdAg4AALAdAg4AALAdAg4AALAdAg4AALAdAg4AALAdAg4AALAdAg4AALAdAg4AALCd/w+3CtAbKdlL6QAAAABJRU5ErkJggg==", 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "make_uniform_series_plot(16)" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0, 0.5, 'Frequency')" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def make_uniform_series_plot_around_0(n, linestyle):\n", + " uniform_series = np.array(\n", + " [sum(random.uniform(-1, 1) for _ in range(n))/n for _ in range(population_size)])\n", + " plt.hist(uniform_series, bins=200, histtype='step', label=f\"n={n}\", linestyle=linestyle, color='black')\n", + "make_uniform_series_plot_around_0(1, 'dotted')\n", + "make_uniform_series_plot_around_0(2, 'dashed')\n", + "make_uniform_series_plot_around_0(4, 'solid')\n", + "plt.vlines([0], [0], [1400], linestyles='dashed', colors='black')\n", + "# sl = 1/np.sqrt(6)\n", + "# plt.vlines([-sl, sl], [0, 0], [1400, 1400], linestyles='dotted', colors='red')\n", + "plt.legend()\n", + "plt.gca().set_xlabel(\"Value\")\n", + "plt.gca().set_ylabel(\"Frequency\")" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "x = np.linspace(-1, 1, 101)\n", + "def get_triangle_pdf(x, a=-1, b=1, c=0):\n", + " return np.where(x < c, (x - a) / (c - a), (b - x) / (b - c))\n", + "\n", + "plt.plot(x, get_triangle_pdf(x))\n", + "plt.vlines([0, -1/np.sqrt(6), 1/np.sqrt(6)], [0, 0, 0], [1, 1, 1], linestyles='dashed', colors='black')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 78, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "x = np.linspace(-1, 1, 101)\n", + "def get_symmetric_triangle_pdf(x, b=1, c=0):\n", + " return ((b - c) - np.abs(x - c))/ ((b - c)**2)\n", + "\n", + "plt.plot(x, get_symmetric_triangle_pdf(x), label='triangle')\n", + "plt.plot(x, np.full(x.shape, 0.5), label='uniform')\n", + "plt.plot(x, (x)**2, label='parabola')\n", + "plt.legend()\n", + "plt.vlines(0, 0, 1, linestyles='dashed', colors='black')\n", + "# plt.vlines([0, -1/np.sqrt(6), 1/np.sqrt(6)], [0, 0, 0], [1, 1, 1], linestyles='dashed', colors='black')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import math\n", + "# Draw the probability distribution for the sum of four random variables divided by 4\n", + "x = np.linspace(-1, 1, 101)\n", + "# y is the probability density function for the sum of four random variables divided by 4\n", + "# each point is the probability of U1 + U2 + U3 + U4 = x\n", + "y = 1/math.factorial(3) * sum((-1)**k _ for k in range(4))" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "modelling-space-PK-9Kbkb-py3.9", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.15" + }, + "orig_nbformat": 4, + "vscode": { + "interpreter": { + "hash": "0e849ea89ee47e1132ea7296f1ee1190d374e3d2d90c5960d8a36248408ee6b5" + } + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/ch-6/8-exercises/cad exercise/Robot.FCStd1 b/ch-6/8-exercises/cad exercise/Robot.FCStd1 deleted file mode 100644 index 88e2ce84ac4b6ea14334ba2762a3caa228bf069a..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 202295 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