4. Let (X,Y) have the following joint density function: 12y? 0
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Problem 1P
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![4. Let \((X,Y)\) have the following joint density function:
\[
f(x, y) =
\begin{cases}
12y^2 & 0 \leq y \leq x \leq 1 \\
0 & \text{otherwise}
\end{cases}
\]
a. Show this a valid joint probability density function.
b. Find the marginal distribution of \(Y\), \(f(y)\).
c. Find the conditional distribution of \(X\) given \(Y=y\), \(f(x|y)\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff0d90012-896b-4f52-8f0b-e38034636c35%2F8e482e7b-70b2-4ae4-b9f5-bacc4da7a115%2Fa4ii23i_processed.png&w=3840&q=75)
Transcribed Image Text:4. Let \((X,Y)\) have the following joint density function:
\[
f(x, y) =
\begin{cases}
12y^2 & 0 \leq y \leq x \leq 1 \\
0 & \text{otherwise}
\end{cases}
\]
a. Show this a valid joint probability density function.
b. Find the marginal distribution of \(Y\), \(f(y)\).
c. Find the conditional distribution of \(X\) given \(Y=y\), \(f(x|y)\).
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