Suppose that discrete random variable A has 10, 3, 12) as its possible outcomes (each of which are equally likely to occur) with ux = 5 and of = 26. For random samples (with replacement) of size n = 3, the median X and mean X are also random variables whose distributions are given by: X = 0 3 12 Ax) = P(X = $) 7/27 13/27 7/27 and X = 0 1 2 3 4 5 6 8 9 12 Ax) = P(X = X) 1/27 3/27 3/27 1/27 3/27 6/27 3/27 3/27 3/27 1/27 respectively. a. Use expectation to determine My and - (the mean and variance of the sampling distribution of A ) to 3 decimals. Show the steps in your calculations. b. Use expectation to determine / and of (the mean and variance of the sampling distribution of X ) to 3 decimals (where necessary). State the summations to be calculated and the final results (i.e. intermediate steps are not required). c. Verify the result in part (b) using the Central Limit Theorem