Consider two random variables with the following pdfs: X ~ N(3, 4) Y~N (5,9) Suppose X and Y are independent. What is the pdf of the random variable Z=Y-X?

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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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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Consider two random variables with the following pdfs:
X~ N(3, 4)
Y~ N(5,9)
Suppose X and Y are independent. What is the pdf of the random variable
Z=Y - X?
Transcribed Image Text:Consider two random variables with the following pdfs: X~ N(3, 4) Y~ N(5,9) Suppose X and Y are independent. What is the pdf of the random variable Z=Y - X?
Expert Solution
Step 1: Given information:

The random variables X and Yare independent. 

The pdf of random variables are, 
X space tilde N open parentheses mu subscript x equals 3 comma space sigma subscript x squared equals 4 close parentheses

Y space tilde N open parentheses mu subscript y equals 5 comma space sigma subscript y squared equals 9 close parentheses

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