a) Determine the values of the population mean and the population variance.
b) Suppose we use an SRSWOR of size $n=4$, list all the possible samples of size $4$. What is the probability for each sample to be selected? Determine the distribution of the sample mean.
c) Using the distribution of the sample mean, compute the following quantities: Expectation of sample mean, variance of sample mean, bias of sample mean and MSE of sample mean for this sampling plan.
For parts (a) and (b), I am able to find the answers easily using R code. I am stuck at part (c), since I could not figure out what is the distribution of the sample mean. I am guessing the expectation of sample mean is the same as the population mean in part a. I am not sure how to proceed to find variance of sample mean.