Question: Setting 1 for Heads and 0 for Tails, the outcome X of a flip of a coin can be thought of as resulting from a simple random selection of one number from {0, 1}.

(a) Compute the variance σ²_x of X.

(b) The possible samples of size two, taken with replacement from the population {0, 1}, are {0, 0},{0, 1},{1, 0},{1, 1}. Compute the sample variance for each of the possible four samples.

(c) Consider the statistical population consisting of the four sample variances obtained in part (b), and let Y denote the random variable resulting from a simple random selection of one number from this statistical population. Compute E(Y).

(d) Compare σ²_x and E(Y). If the sample variance in part (b) was computed according to a formula that divides by n instead of n - 1, how would σ²_x and E(Y) compare?