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Let X1 and X2 be two normal random variables. Suppose X1 is distributed as N(µ1,o3), and X2 is distributed as N(µ2,03). Suppose X1 and X2 are independent. 1. Let Y1 = 3X1. Find the distribution of Y1 and prove it. 2. Let Y2 = X1 – X2. Find the distribution of Y2 and prove it. (Hint: One can use the moment generating function of normal distribution.)

Let X1 and X2 be two normal random variables. Suppose X1 is distributed as N(µ1,o3), and X2 is distributed as N(µ2,03). Suppose X1 and X2 are independent. 1. Let Y1 = 3X1. Find the distribution of Y1 and prove it. 2. Let Y2 = X1 – X2. Find the distribution of Y2 and prove it. (Hint: One can use the moment generating function of normal distribution.)

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Let X1 and X2 be two normal random variables. Suppose X1 is distributed as N(u1, 07), and X2 is distributed as N(u2,03). Suppose X1 and X2 are independent. 1. Let Y1 = 3X1. Find the distribution of Y1 and prove it. 2. Let Y2 = X1 – X2. Find the distribution of Y2 and prove it. (Hint: One can use the moment generating function of normal distribution.)
Transcribed Image Text:Let X1 and X2 be two normal random variables. Suppose X1 is distributed as N(u1, 07), and X2 is distributed as N(u2,03). Suppose X1 and X2 are independent. 1. Let Y1 = 3X1. Find the distribution of Y1 and prove it. 2. Let Y2 = X1 – X2. Find the distribution of Y2 and prove it. (Hint: One can use the moment generating function of normal distribution.)
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