1. (10 pts.) Suppose that Y1, ...; Ym are independent and identically distribute with common probability mass function f (y) = To for y c {0, 1, ...,9 ). (a) Compute E(Y,) and var(Y,) for any i = 1, ...,n (these values are the same for all i) (b) Suppose you do not know what the common distribution of these ran dom variables is, but you are given a data set of observations, y* {8, 0, 5, 5, 9, 2, 7, 6, 3, 5}. Estimate the expected value and variance. (c) Construct a 95% interval estimate (a confidence interval) for E(Y,) (se note at end of assignment). (d) What result (name of the result) is the basis for the methodology yo used in constructing the interval of part (c)? (e) Do you think you can justify using the result from part (d)? Why or why not