Question 4 Let X and Y be bivariate Gaussian random variables with: • E[X] = 1, E[Y] = 2, • Var[X] = 4, Var[Y] =9 • Cov[X, Y] = -2. a) What is the probability density function (pdf) of X? b) What is P[ Y < E[Y]] ? c) What are the mean and variance of Z = 2X – Y + 1?

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Q: Find the density of Z

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A: we have given that  V(X)=V(Y) and C(X,Y)=C(Y,X)   ,C(X,X)=V(X) ,  C(Y,Y)=V(Y)

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