Let Z1 and Z2 be independent standard normal random variables and U1 = Z1 and U2 = Z1 +
Chapter 6, Problem 6.65(choose chapter or problem)
Let Z1 and Z2 be independent standard normal random variables and U1 = Z1 and U2 = Z1 + Z2. a Derive the joint density of U1 and U2. b Use Theorem 5.12 to give E(U1), E(U2), V(U1), V(U2), and Cov(U1, U2). c Are U1 and U2 independent? Why? d Refer to Section 5.10. Show that U1 and U2 have a bivariate normal distribution. Identify all the parameters of the appropriate bivariate normal distribution.
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