Discuss the below:
Q: Let X1 and X2 be independent normal random variables, X1 n(μi,σi2), and let
Y1 = X1 and Y2 = X1+X2
a) Show that Y1 and Y2 are bivariate normal.
b) What are the means, variances, and correlation coefficient of Y1 and Y2?
c) Find the conditional distribution of Y2 given Y1=y.