STAT 359/563 A01 (Spring 2018)
Assignment 2:
Due 1:00pm, February 19
1. (14 marks) Use R to take 10, 100, 500 samples of size 10, 30, 60 from the following
two distributions:(i) Binomial(1, 0.85),(ii) t distribution with df=3.(a) (8 marks) Investigate how the Central Limit Theorem works when samplingfrom the above distributions, and for each sample size.— Write an R function to simulate the distribution of the sample mean. TheR function has three arguments, the number of samples (N), the sample size(n), and the distribution. In the function, you generate N samples from thegiven distribution and each sample has size n. Then you compute N samplemeans. The output of the function includes a histogram of the sample meansand the normality test for the sample means.— Use histograms to illustrate the distributions of the sample mean for eachsample size, number of samples, and distribution.— Organize the 18 (3x3x2) histograms into 2 pages for your solution.(b) (2 marks) What do you notice as sample size increases?(c) (2 marks) What do you notice as the number of samples increases?