HelloI need your help please take a look for the probability questionQuestion 1: Let X and Y be independent normal randomvariables with distributions N(2, 9) and N(2, 4], respectively. (a) Find lE(2Y X).(b) Find the standard deviation ngwx. (cl Find W21 > X + Tl.: Let X1, X2 and X3 be mutually independent Question 2 : Let Var(X) : 9, Var(Y) : 25 and Var(X+Y) : 10 (we do not assume independence here). Find Var(2X _ 31 + 4). Question 3: Let X1, X2 and X3 be mutually independentrandom variables, all with distribution U(0,1). De?ne two other random variables byU:X1 4X2, V:2X2X3. (a) Find ]E(U) and ]E(V). (b) Find Var(U) and Var(V). (c) Find Cov(U,V). (d) Find p(U, V). Comment on the sign and strength ofthc correlation.
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