Please help with this practice problem Consider two random variables with the following probability density functions (pdfs):\[ X \sim \mathcal{N}(3, 4) \]\[ Y \sim \mathcal{N}(5, 9) \]Suppose $ X $ and $ Y $ are independent. What is the pdf of the random variable $ Z = Y - X $?

The random variables and are independent. The pdf of random variables are,

Answered: Consider two random variables with the…

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?

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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Question

Please help with this practice problem

Consider two random variables with the following probability density functions (pdfs):

\[ X \sim \mathcal{N}(3, 4) \]

\[ Y \sim \mathcal{N}(5, 9) \]

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 $Y$ are 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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