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2.0.3 Problem 3: Central Limit Theorem Here we will verify the Central Limit Theorem and reproduce plots similar to those from Wikipedia (https://en.wikipedia.org/wiki/Central_limit_theorem#/media/File:Dice_sum_central_limit_thed a) Write a function that returns n integer random numbers, uniformly distributed between 1 and 6, inclusively. This represents n throws of a fair 6-sided die. The value that comes up at each throw will be called the "score". b) Generate a distribution of 1000 dice throws and plot it as a histogram normalized to unit area. Compute the mean ₁ and standard deviation o₁ of this distribution. Compare your numerical result to the analytical calculation. c) Generate 1000 sets of throws of N = 2, 3, 4, 5, 10, 20, 30 dice, computing the total sum of dice scores for each set. For each value of N, plot the distribution of total scores, and compute the mean N and standard deviation ON of each distribution. This should be similar to the plot at the link above.

2.0.3 Problem 3: Central Limit Theorem Here we will verify the Central Limit Theorem and reproduce plots similar to those from Wikipedia (https://en.wikipedia.org/wiki/Central_limit_theorem#/media/File:Dice_sum_central_limit_thed a) Write a function that returns n integer random numbers, uniformly distributed between 1 and 6, inclusively. This represents n throws of a fair 6-sided die. The value that comes up at each throw will be called the "score". b) Generate a distribution of 1000 dice throws and plot it as a histogram normalized to unit area. Compute the mean ₁ and standard deviation o₁ of this distribution. Compare your numerical result to the analytical calculation. c) Generate 1000 sets of throws of N = 2, 3, 4, 5, 10, 20, 30 dice, computing the total sum of dice scores for each set. For each value of N, plot the distribution of total scores, and compute the mean N and standard deviation ON of each distribution. This should be similar to the plot at the link above.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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2.0.3 Problem 3: Central Limit Theorem Here we will verify the Central Limit Theorem and reproduce plots similar to those from Wikipedia (https://en.wikipedia.org/wiki/Central_limit_theorem#/media/File:Dice_sum_central_limit_theorer a) Write a function that returns n integer random numbers, uniformly distributed between 1 and 6, inclusively. This represents n throws of a fair 6-sided die. The value that comes up at each throw will be called the "score". b) Generate a distribution of 1000 dice throws and plot it as a histogram normalized to unit area. Compute the mean ₁ and standard deviation o₁ of this distribution. Compare your numerical result to the analytical calculation. c) Generate 1000 sets of throws of N = 2, 3, 4, 5, 10, 20, 30 dice, computing the total sum of dice scores for each set. For each value of N, plot the distribution of total scores, and compute the mean and standard deviation on of each distribution. This should be similar to the plot at the link above. d) Plot the standard deviation oN as a function of N. Does it follow the Central Limit Theorem?
Transcribed Image Text:2.0.3 Problem 3: Central Limit Theorem Here we will verify the Central Limit Theorem and reproduce plots similar to those from Wikipedia (https://en.wikipedia.org/wiki/Central_limit_theorem#/media/File:Dice_sum_central_limit_theorer a) Write a function that returns n integer random numbers, uniformly distributed between 1 and 6, inclusively. This represents n throws of a fair 6-sided die. The value that comes up at each throw will be called the "score". b) Generate a distribution of 1000 dice throws and plot it as a histogram normalized to unit area. Compute the mean ₁ and standard deviation o₁ of this distribution. Compare your numerical result to the analytical calculation. c) Generate 1000 sets of throws of N = 2, 3, 4, 5, 10, 20, 30 dice, computing the total sum of dice scores for each set. For each value of N, plot the distribution of total scores, and compute the mean and standard deviation on of each distribution. This should be similar to the plot at the link above. d) Plot the standard deviation oN as a function of N. Does it follow the Central Limit Theorem?
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