4. Let -1 ≤ x ≤ 1 be a continuous random variable with density (pdf) given by 1- x 2 fx(x) = (a) Let Y = |X|. Find the range of Y and a formula for the density fy(y). (b) Let Z = X². Find the range of Z and a formula for the density fz(z).
4. Let -1 ≤ x ≤ 1 be a continuous random variable with density (pdf) given by 1- x 2 fx(x) = (a) Let Y = |X|. Find the range of Y and a formula for the density fy(y). (b) Let Z = X². Find the range of Z and a formula for the density fz(z).
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Solve in detial please. Thank you
![**Problem 4**
Let \( -1 \leq X \leq 1 \) be a continuous random variable with a probability density function (pdf) given by:
\[
f_X(x) = \frac{1-x}{2}.
\]
**(a)** Let \( Y = |X| \). Find the range of \( Y \) and a formula for the density \( f_Y(y) \).
**(b)** Let \( Z = X^2 \). Find the range of \( Z \) and a formula for the density \( f_Z(z) \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F48ceae03-ce82-43df-b816-3449c4a6aa24%2F12aadf92-299f-4843-947a-5a3d806d380c%2F3zk1yv_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 4**
Let \( -1 \leq X \leq 1 \) be a continuous random variable with a probability density function (pdf) given by:
\[
f_X(x) = \frac{1-x}{2}.
\]
**(a)** Let \( Y = |X| \). Find the range of \( Y \) and a formula for the density \( f_Y(y) \).
**(b)** Let \( Z = X^2 \). Find the range of \( Z \) and a formula for the density \( f_Z(z) \).
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