5. Overlapping Counts Consider a sequence of i.i.d. Bernoulli (p) trials. Consider the three variables X, Y, and V defined by: . X is the number of successes in trials 1 through 100 . Y is the number of successes in trials 51 through 100 - V is the number of successes in trials 51 through 150 a) For each of X . Y, and V, say what the distribution is and provide the parameters. b) Fix k in the range 0, 1, . .. , 100 and find the conditional distribution of Y given X = k. Recognize this as a famous one and provide the parameters. c) Find the least squares predictor of Y based on X and say whether it is a linear function of X. (If it is, then the best linear predictor is in fact the best among all predictors.) Find Var(Y | X). d) Find E(V | X). Var(V | X), and the correlation r(X, V)