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Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 32E

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Suppose that {X1, X2, X3} are statistically independent Gaussian random variables with
P₁ = E{X₂} = 0 and var (X₁) = o2 for i = 1, 2, 3.
a) Are {X₁, X2, X3} jointly Gaussian? Please explain. Find the joint pdf of the three
random variables.
b) Let
* (X) = (17) (X). Are {Y₁, Y2} statistically independent? Please
Y₂
explain.
c) Find cov(Y2, X2).

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