5. Let X, Y be iid random variables each with density fx(x) = for x > 1 and zero otherwise. (a) (b) Find the density of Z = Y/X. Find E[√Z].
5. Let X, Y be iid random variables each with density fx(x) = for x > 1 and zero otherwise. (a) (b) Find the density of Z = Y/X. Find E[√Z].
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![### Problem Statement
Let \( X, Y \) be independent and identically distributed (iid) random variables each with the density function:
\[
f_X(x) = \frac{1}{x^2} \quad \text{for } x > 1
\]
and zero otherwise.
#### Questions:
(a) Find the density of \( Z = \frac{Y}{X} \).
(b) Find \( \mathbb{E}[\sqrt{Z}] \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fff93c792-abd7-4eff-ba98-8a1e3cbd1351%2F13c72ccb-0a4d-4707-abf4-2d608b93f9d4%2Ficqgvka_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Statement
Let \( X, Y \) be independent and identically distributed (iid) random variables each with the density function:
\[
f_X(x) = \frac{1}{x^2} \quad \text{for } x > 1
\]
and zero otherwise.
#### Questions:
(a) Find the density of \( Z = \frac{Y}{X} \).
(b) Find \( \mathbb{E}[\sqrt{Z}] \).
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