7. [10] Suppose that Xi, i = 1,..., 5, are independent normal random variables, where X1, X2 and X3 have the same distribution N(1, 2) and X4 and X5 have the same distribution N(-1, 1). Let (a) Find V(X5 - X3). 1 = √(x1 + x2) — — (Xx3 + x4 + X5). (b) Find the distribution of Y. (c) Find Cov(X2 - X1, Y). -

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 31E
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7. [10] Suppose that Xi, i = 1,..., 5, are independent normal random variables, where
X1, X2 and X3 have the same distribution N(1, 2) and X4 and X5 have the same
distribution N(-1, 1). Let
(a) Find V(X5 - X3).
1
= √(x1 + x2) — — (Xx3 + x4 + X5).
(b) Find the distribution of Y.
(c) Find Cov(X2 - X1, Y).
-
Transcribed Image Text:7. [10] Suppose that Xi, i = 1,..., 5, are independent normal random variables, where X1, X2 and X3 have the same distribution N(1, 2) and X4 and X5 have the same distribution N(-1, 1). Let (a) Find V(X5 - X3). 1 = √(x1 + x2) — — (Xx3 + x4 + X5). (b) Find the distribution of Y. (c) Find Cov(X2 - X1, Y). -
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