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- Let X be a standard normal RV. Suppose Y = 2X+3 and Z = -X+6. a) Find the covariance between Y and Z b) Find the correlation coefficient between Y and Z1. Consider the Gaussian distribution N (m, σ2).(a) Show that the pdf integrates to 1.(b) Show that the mean is m and the variance is σ.let X and Y be independent standard normal random variables. Determine the pdf of W = X^2 + Y^2. Find the mean and the variance of U= (1/2)W