Question: 2. Suppose (X1, X2) ~ bivariate normal(0, 0, 1, 1, p). (a) Show that X1 + X2 and X1 - X2 are independent normal r.v.'s.

2. Suppose (X1, X2) ~ bivariate normal(0, 0, 1, 1, p).

2. Suppose (X1, X2) ~ bivariate normal(0, 0, 1, 1, p). (a) Show that X1 + X2 and X1 - X2 are independent normal r.v.'s. (b) Let Y1 = alX1 + a2X2 + a3, Y2 = biX1 + b2X2 + 63. Find the joint distribution of (Y1, Y2). Given what we know, you do not need to work out the joint pdf! Just identify the distribution and its parameters. In particular, determine Corr(Y1, Y2)

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