Question: Z1 and Z2 are independent random variables. Each random variable has a standard normal distribution. Define X = Z1 +3Z2 and Y = Z1 +Z2.

Z1 and Z2 are independent random variables. Each random variable has a standard normal distribution. Define X = Z1 +3Z2 and Y = Z1 +Z2. What is the distribution of X? What is the distribution of Y ? It can be proved that the joint distribution of (X; Y ) is a bivariate normal. What are the parameters of this distribution? In other words, compute E(X), E(Y), Var(X), Var(Y), and Corr(X;Y). (10 points)

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