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Consider a sequence of i.i.d. Bernoulli (12) trials. Consider the three variables X , Y. and V defined by: 0 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 I X), Var(V I X), and the correlation r(X, V)