1 1 Suppose that 2 E N(0,1) and that X = 22. Moreover, we have that for another random variable Y, 1 fylx=x (y) = Exże 3

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1 1 Suppose That 2 E N 0 1 And That X 22 Moreover We Have That For Another Random Variable Y 1 Fylx X Y Exze 3 1 (56.03 KiB) Viewed 186 times

1 1 Suppose that 2 E N(0,1) and that X = 22. Moreover, we have that for another random variable Y, 1 fylx=x (y) = Exże 3xy?, ;-0 < y < too. 27 (a) [6 points] Show that X EXP(1) by deriving the moment generating function of X. That is, compute 4x(t) = EetX = Eetz?. (You are NOT allowed to directly plug in the moment generating function of the chi-square distribution by simply stating that “x?(1) is the square of standard normal”.) (b) [6 points] Compute E(Y|X = x) and E[E(Y|X)] ©) [8 points) Find the distribution of Y.