Let B and B be Bernoulli random variables with E [B] = 0.3, E [B] = 0.2, Let X, X2, X3 be exponential random variables with distributions f(x) = e-*, f(x) = 2e-2x, The random variable Y is defined as (a) Are B and B independent? Explain why. (b) Find the joint pmf of B and B. B = 0 B = 1 B = 0 B2 1 = Cov (B, B)= 0.04. Y = B B X + B (1 B) X2 + (1 B) B2 X3. -3x f3(x) = 3e *, x 0. (c) Find the pdf of Y. (You might want to try conditioning Y on B and B.)