Q9: Let X and Y be independent normal random variables with means μr, Hy, and variances o, o, respectively. Use the MGF approach to show that Z=X+Y is a normal random variable with mean + Hy and variance o2 +0².
Q9: Let X and Y be independent normal random variables with means μr, Hy, and variances o, o, respectively. Use the MGF approach to show that Z=X+Y is a normal random variable with mean + Hy and variance o2 +0².
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Transcribed Image Text:Q9:
Let X and Y be independent normal random variables with means µr,
Hy, and variances o, o, respectively.
Use the MGF approach to show that Z=X+Y is a normal random variable
with mean μμy and variance o² +0.
Expert Solution
Step 1
Given
X~N(μx, σ2x) and Y~N(μy, σ2y )
- X and Y are independent.
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