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- Let X and Y be independent Exp(2) random variables. Define W = X + Y. a) Determine the correlation between X and W. The joint pdf of X and W is: fx,w(x, w) = 1^(2) e^(-1w) I{OLet X and Y are 2 independent random variables N (0,1) Questions: how to find E(X), E(Y), E(X^2), E(Y^2)? Thank youthe random variable Y is such that : E(2Y+3)=6 and Var(2-3Y)=11 find E(Y^2)Let X₁ and X₂ be two independent random variables with normal distributions N (1,9) and N(-3,16), respectively. Find the moment generating function of Y= X₁ + X₂. What distribution is associated with this moment generating function?Let Y~Po(1) be a poisson distributed variable with parameter 1 = 1. Suppose that, designated on Y, X is X, i = 1, ...,7 independent random variable with conditional distribution P(X;|Y) = Bin(N, 1/3) Determine the variance of the sum X = X1+...+X,Suppose that f (x) = e=* for 0 < x Determine the mean and variance of the random variable.