240 lines
8.7 KiB
Plaintext
240 lines
8.7 KiB
Plaintext
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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [],
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"source": [
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"import scipy.stats as stats\n",
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"import numpy as np\n",
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"import pandas as pd\n",
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"\n",
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"Dat = pd.read_csv('DataLoL.csv')\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**Question 2**"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"(hypergeometric) Probability of observing between 21 and 40 cases of breast cancer: 0.664806\n",
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"(hypergeometric) Probability of observing more than 60 cases of breast cancer: 0.000352\n",
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"(hypergeometric) Probability of observing less than or equal to 30 cases of breast cancer: 0.108530\n",
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"(hypergeometric) Probability of observing exactly 35 cases of breast cancer: 0.059625\n"
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]
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}
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],
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"source": [
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"# Given parameters\n",
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"n = 36121175 # the female population of Thailand ()\n",
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"r = round((38 / 100000) * n) # the number of women in Thailand with breast cancer\n",
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"k = 100000 # sample size\n",
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"\n",
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"# Create the hypergeometric distribution object\n",
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"rv = stats.hypergeom(n, r, k)\n",
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"\n",
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"# Calculate the probability using hypergeometric distribution\n",
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"prob_21_to_40 = rv.cdf(40) - rv.cdf(20) # (a)\n",
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"\n",
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"prob_more_than_60 = 1 - rv.cdf(60) # (b)\n",
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"\n",
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"prob_less_than_equal_30 = rv.cdf(30) # (c)\n",
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"\n",
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"prob_exactly_35 = rv.pmf(35) # (d)\n",
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"\n",
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"# Print the results\n",
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"print(f\"(hypergeometric) Probability of observing between 21 and 40 cases of breast cancer: {prob_21_to_40:.6f}\")\n",
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"print(f\"(hypergeometric) Probability of observing more than 60 cases of breast cancer: {prob_more_than_60:.6f}\")\n",
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"print(f\"(hypergeometric) Probability of observing less than or equal to 30 cases of breast cancer: {prob_less_than_equal_30:.6f}\")\n",
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"print(f\"(hypergeometric) Probability of observing exactly 35 cases of breast cancer: {prob_exactly_35:.6f}\")"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**Question 3**"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"(Binomial) Probability of observing between 21 and 40 cases of breast cancer: 0.664631\n",
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"(Binomial) Probability of observing more than 60 cases of breast cancer: 0.000359\n",
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"(Binomial) Probability of observing less than or equal to 30 cases of breast cancer: 0.108849\n",
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"(Binomial) Probability of observing exactly 35 cases of breast cancer: 0.059569\n"
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]
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}
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],
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"source": [
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"# Given parameters\n",
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"n = 36121175 # the female population of Thailand\n",
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"r = round((38 / 100000) * n) # the number of women in Thailand with breast cancer\n",
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"k = 100000 # sample size\n",
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"p = r / n # Probability of success\n",
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"\n",
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"# calculate the probability using binomial approximation\n",
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"prob_21_to_40_binom = stats.binom.cdf(40, k, p) - stats.binom.cdf(20, k, p) # (a)\n",
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"\n",
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"prob_more_than_60_binom = 1 - stats.binom.cdf(60, k, p) # (b)\n",
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"\n",
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"prob_less_than_equal_30_binom = stats.binom.cdf(30, k, p) # (c)\n",
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"\n",
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"prob_exactly_35_binom = stats.binom.pmf(35, k, p) # (d)\n",
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"\n",
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"# Print the results\n",
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"print(f\"(Binomial) Probability of observing between 21 and 40 cases of breast cancer: {prob_21_to_40_binom:.6f}\")\n",
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"print(f\"(Binomial) Probability of observing more than 60 cases of breast cancer: {prob_more_than_60_binom:.6f}\")\n",
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"print(f\"(Binomial) Probability of observing less than or equal to 30 cases of breast cancer: {prob_less_than_equal_30_binom:.6f}\")\n",
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"print(f\"(Binomial) Probability of observing exactly 35 cases of breast cancer: {prob_exactly_35_binom:.6f}\")\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**Question 4**"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"(Poisson) Probability of observing between 21 and 40 cases of breast cancer: 0.664607\n",
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"(Poisson) Probability of observing more than 60 cases of breast cancer: 0.000360\n",
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"(Poisson) Probability of observing less than or equal to 30 cases of breast cancer: 0.108893\n",
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"(Poisson) Probability of observing exactly 35 cases of breast cancer: 0.059561\n"
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]
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}
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],
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"source": [
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"# Given parameters\n",
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"k = 100000 # Sample size\n",
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"n = 36121175 # Total female population of Thailand\n",
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"r = round((38 / 100000) * n) # Estimated number of women with breast cancer\n",
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"p = r / n # Probability of success\n",
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"\n",
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"# Calculate lambda for Poisson approximation\n",
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"lambda_poisson = k * p\n",
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"\n",
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"# calculate the probability using poisson approximation\n",
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"prob_21_to_40_poisson = stats.poisson.cdf(40, lambda_poisson) - stats.poisson.cdf(20, lambda_poisson) # (a)\n",
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"\n",
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"prob_more_than_60_poisson = 1 - stats.poisson.cdf(60, lambda_poisson) # (b)\n",
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"\n",
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"prob_less_than_equal_30_poisson = stats.poisson.cdf(30, lambda_poisson) # (c)\n",
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"\n",
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"prob_exactly_35_poisson = stats.poisson.pmf(35, lambda_poisson) # (d)\n",
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"\n",
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"# Print the results\n",
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"print(f\"(Poisson) Probability of observing between 21 and 40 cases of breast cancer: {prob_21_to_40_poisson:.6f}\")\n",
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"print(f\"(Poisson) Probability of observing more than 60 cases of breast cancer: {prob_more_than_60_poisson:.6f}\")\n",
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"print(f\"(Poisson) Probability of observing less than or equal to 30 cases of breast cancer: {prob_less_than_equal_30_poisson:.6f}\")\n",
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"print(f\"(Poisson) Probability of observing exactly 35 cases of breast cancer: {prob_exactly_35_poisson:.6f}\")\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**Question 5**"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Probability of X happens before the 7th game: 0.794816\n",
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"Probability of X happens at the 7th game: 0.047604\n",
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"Probability of X happens after the 7th game: 0.157579\n",
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"Probability of Y happens befor the 7th game: 0.277992\n",
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"Probability of Y happens at the 7th game: 0.038150\n",
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"Probability of Y happens after the 7th game: 0.683857\n"
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]
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}
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],
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"source": [
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"# number of game in Dat\n",
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"totalGame = len(Dat)\n",
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"\n",
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"# calculate probability of team blue wins and kills the dragon\n",
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"probBlueWinsAndDragons = len(Dat[(Dat['blueWins'] == 1) & (Dat['blueDragons'] == 1)]) / totalGame\n",
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"\n",
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"# calculate probability of team blue wins, kills the dragon and kills the heralds\n",
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"probBlueWinsAndDragonsAndHeralds = len(Dat[(Dat['blueWins'] == 1) & (Dat['blueDragons'] == 1) & (Dat['blueHeralds'] == 1)]) / totalGame\n",
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"\n",
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"# calculate probability of the event X\n",
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"probXLessthan7 = stats.geom.cdf(6, probBlueWinsAndDragons) # (a)\n",
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"\n",
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"probXExactly7 = stats.geom.pmf(7, probBlueWinsAndDragons) # (b)\n",
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"\n",
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"probXMorethan7 = 1 - stats.geom.cdf(7, probBlueWinsAndDragons) # (c)\n",
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"\n",
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"# calculate probability of the event Y\n",
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"probYLessthan7 = stats.geom.cdf(6, probBlueWinsAndDragonsAndHeralds) # (a)\n",
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"\n",
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"probYxactly7 = stats.geom.pmf(7, probBlueWinsAndDragonsAndHeralds) # (b)\n",
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"\n",
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"probYMorethan7 = 1 - stats.geom.cdf(7, probBlueWinsAndDragonsAndHeralds) # (c)\n",
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"\n",
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"# Print the results\n",
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"print(f\"Probability of X happens before the 7th game: {probXLessthan7:.6f}\")\n",
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"print(f\"Probability of X happens at the 7th game: {probXExactly7:.6f}\")\n",
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"print(f\"Probability of X happens after the 7th game: {probXMorethan7:.6f}\")\n",
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"print(f\"Probability of Y happens befor the 7th game: {probYLessthan7:.6f}\")\n",
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"print(f\"Probability of Y happens at the 7th game: {probYxactly7:.6f}\")\n",
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"print(f\"Probability of Y happens after the 7th game: {probYMorethan7:.6f}\")"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.12.5"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}
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