2. Expectation of a mixed random variable (12 points). Consider the mixed r.v. with the cdf sketched in Figure I. (a) Express this r.v. in terms of a continuous r.v. Y and a discrete r.v. Z in the form X = Y with probability (1 - p), Z with probability p. and find p, the pdf of Y, and the pmf of Z. (b) Use the law of total expectation to find E(X ) and Var(X).\f