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i) If U, and U, each have a normal distribution with mean 0 and variance 202. Furthermore, my, (t) = et)^20 for i = 1,2. Show that U, and U, are independent. Hint: Use moment-generating functions.

i) If U, and U, each have a normal distribution with mean 0 and variance 202. Furthermore, my, (t) = et)^20 for i = 1,2. Show that U, and U, are independent. Hint: Use moment-generating functions.

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 19E
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Kindly assist with question 2, (i)

QUESTION 2 i) If U, and U, each have a normal distribution with mean 0 and variance 20².Furthermore, my (t) = e(t;)^20 for i = 1,2. Show that U, and U, are mui independent. Hint: Use moment-generating functions. ii) where Z is a normal random variable and x² is chi-square Let T = with n degree of freedom. Use a moment-generating approach to find f(t)
Transcribed Image Text:QUESTION 2 i) If U, and U, each have a normal distribution with mean 0 and variance 20².Furthermore, my (t) = e(t;)^20 for i = 1,2. Show that U, and U, are mui independent. Hint: Use moment-generating functions. ii) where Z is a normal random variable and x² is chi-square Let T = with n degree of freedom. Use a moment-generating approach to find f(t)
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