4. Consider rolling a fair, six-sided die. (a) Find the expected value and variance for the number of dots on the die th

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4 Consider Rolling A Fair Six Sided Die A Find The Expected Value And Variance For The Number Of Dots On The Die Th 1 (23.72 KiB) Viewed 37 times

4. Consider rolling a fair, six-sided die. (a) Find the expected value and variance for the number of dots on the die that occur from one roll. (b) Find the expected value and variance for the average number of dots that occur from 24 rolls. (c) Use the Central Limit Theorem to describe the approximate distribution for the average of dots occurring from 24 rolls. (d) Use part (e) along with a numerical integration to estimate the probability that the average number is between 3.0 and 4.0. (e) Write a MATLAB file that rolls a die 24 times, and outputs the average number of dots that occur. Run this program 1000 times and generate a histogram for the "average number of dots". Plot the normal approximation density function on the same axes.