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question 8 aurose that in a sman island, all families have either 0, 1, or 2 children with probabilities 0-2; Sup and 0.3 respectively . Assume that the probability of having a boy or a girl is the same. Let the Of dom variable A be the number of boys and the random Variable Y be the number of girls. Compute the joint and the marginal probability mass function of X, and Y. show the answer's steps, then fill the table with the correct values Question 9 Let X be an Exponential random variable, with the moment generating function (MGF): M(t) = (1-0t)-1. (a) Derive the MGF above. (b) Derive E(X) using the MGF. (c) Derive V(X) using the MGF. (d) Find the MGF of Y, where Y = 2X - 3. Question 10 Suppose X1 and X2 are two independent random variables, as below: Xi with p(x) = - for x > 0, and X2 with p(x) = -for x > 0. Where A is a random variable that is uniformly distributed over the interval from 0 to 2. Also let U = X1 - -X2 . Find: (a) E(X2) (b) E(U) (c) V(U)