{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"id": "432a6809",
"metadata": {},
"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
"%matplotlib inline\n",
"import random\n",
"from mxnet import np, npx\n",
"from d2l import mxnet as d2l\n",
"\n",
"npx.set_np()"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "35f930d4",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[0.16666666666666666,\n",
" 0.16666666666666666,\n",
" 0.16666666666666666,\n",
" 0.16666666666666666,\n",
" 0.16666666666666666,\n",
" 0.16666666666666666]"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Vector of probabilities\n",
"fair_probs = [1.0 / 6] * 6\n",
"fair_probs"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "606238a0",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([0, 0, 0, 1, 0, 0], dtype=int64)"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.random.multinomial(1, fair_probs) # Multinimial distribution\n",
"# ^^^ # tries"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "03390a4c",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ 981, 969, 991, 992, 1011, 1056], dtype=int64)"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.random.multinomial(6000, fair_probs) # Distribution of the outcomes"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "c5f61530",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([0.977, 1.031, 0.986, 1.029, 1.005, 0.972])"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.random.multinomial(6000, fair_probs)/1000"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "98cd0b81",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[1, 2, 1, 2, 1, 3],\n",
" [1, 3, 2, 2, 0, 2],\n",
" [2, 2, 1, 1, 3, 1],\n",
" ...,\n",
" [2, 0, 2, 1, 3, 2],\n",
" [1, 4, 0, 3, 0, 2],\n",
" [2, 1, 2, 1, 3, 1]], dtype=int64)"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Plotting probabilities...\n",
"#\n",
"# Perform 500 groups of experiments where each group draws 10 samples\n",
"counts = np.random.multinomial(10, fair_probs, size=500)\n",
"counts"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "3f476243",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 1., 2., 1., 2., 1., 3.],\n",
" [ 2., 5., 3., 4., 1., 5.],\n",
" [ 4., 7., 4., 5., 4., 6.],\n",
" ...,\n",
" [831., 862., 857., 794., 843., 793.],\n",
" [832., 866., 857., 797., 843., 795.],\n",
" [834., 867., 859., 798., 846., 796.]])"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Compute cumulative sum\n",
"cum_counts = counts.astype(np.float32).cumsum(axis=0)\n",
"cum_counts"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "96169075",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[0.1 , 0.2 , 0.1 , 0.2 , 0.1 ,\n",
" 0.3 ],\n",
" [0.1 , 0.25 , 0.15 , 0.2 , 0.05 ,\n",
" 0.25 ],\n",
" [0.13333334, 0.23333333, 0.13333334, 0.16666667, 0.13333334,\n",
" 0.2 ],\n",
" ...,\n",
" [0.16686746, 0.17309237, 0.17208835, 0.15943775, 0.1692771 ,\n",
" 0.15923695],\n",
" [0.16673347, 0.17354709, 0.17174348, 0.15971944, 0.16893788,\n",
" 0.15931864],\n",
" [0.1668 , 0.1734 , 0.1718 , 0.1596 , 0.1692 ,\n",
" 0.1592 ]])"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Compute the probabilities\n",
"estimates = cum_counts / cum_counts.sum(axis=1, keepdims=True)\n",
"estimates"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "2a5085a0",
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
"\n",
"\n",
"\n"
],
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Plot the progression... law of large number visualized...\n",
"\n",
"d2l.set_figsize((6, 4.5))\n",
"\n",
"for i in range(6):\n",
" d2l.plt.plot(estimates[:, i].asnumpy(),\n",
" label=(\"P(die=\" + str(i + 1) + \")\"))\n",
" \n",
"d2l.plt.axhline(y=0.167, color='black', linestyle='dashed')\n",
"d2l.plt.gca().set_xlabel('Groups of experiments')\n",
"d2l.plt.gca().set_ylabel('Estimated probability')\n",
"d2l.plt.legend();"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "9da2d787",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"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": "3.8.13"
}
},
"nbformat": 4,
"nbformat_minor": 5
}