Question: 1. Let X and Y be two continuous random variables. (a) if X and Y are independent, show that they are also uncorrelated. (b) If

1. Let X and Y be two continuous random

1. Let X and Y be two continuous random variables. (a) if X and Y are independent, show that they are also uncorrelated. (b) If X and Y are independent, express Var(X Y) in terms of Var(x) and Var(Y). (c) If X and Y are independent and E(X) = E(Y), are X and Y also orthogonal? (d) For the two continuous random variables X and Y have joint pdf given by fxx (x, y) i, OSX S1, 0 Sys1 otherwise. Show that E(XY) = E(X2)E(Y2). : {

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