Let Y1 and Y2 be independent normally distributed random variables with means 1 and 2
Chapter 5, Problem 5.131(choose chapter or problem)
Let Y1 and Y2 be independent normally distributed random variables with means 1 and 2, respectively, and variances 2 1 = 2 2 = 2. a Show that Y1 and Y2 have a bivariate normal distribution with = 0. b Consider U1 = Y1 + Y2 and U2 = Y1 Y2. Use the result in Exercise 5.130 to show that U1 and U2 have a bivariate normal distribution and that U1 and U2 are independent.
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