Please answer questions 1 and 2 and show work.

1) Consider the population distribution of X as shown below: X A(x) 0.1 8 0.3 10 0.6 Total 1 Samples of size n = 2 will be drawn from this population, by sampling with replacement. a) List all possible samples and find the sample mean (x), the sample variance (s2), the sample standard deviation (s), and the probability for each sample. Note that there will be 9 samples in all. b) Determine the sampling distribution of X. c) Determine the sampling distribution of $2. d) Determine the sampling distribution of the sample standard deviation, S. 2) Using the sampling distribution for X in Question 1 part b, verify that E(X) = M