Question: Let X1 and X2 be independent random variables and let Y1 = Ф1(X1) and Y2 = Ф2(X2). (a) Show that (b) Using (a), show that

Let X1 and X2 be independent random variables and let Y1 = Ф1(X1) and Y2 = Ф2(X2).
(a) Show that


P(Y =r,Y2 = s) = E P(X1 = a, X2 = 6) 1(0)-r t(b)-

(b) Using (a), show that P (Y1 = r, Y2 = s) = P (Y1 = r) P (Y2 = s) so that Y1 and Y2 are independent.

P(Y =r,Y2 = s) = E P(X1 = a, X2 = 6) 1(0)-r t(b)-

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