Let X and Y be two random variables cotinuous with PDF equal to if (x, y) E D fxx(x, y) 0. elsewhere . where D is the region of the plane delimited by three lines: y = 1 (parallel to the r axes), x = 1 (parallel to the y axes), and y = 1- x. Determine 1. the marginal density of fx(x); 2. the conditional density of fY|x; 3. the independence (or dependence) between X and Y.
Let X and Y be two random variables cotinuous with PDF equal to if (x, y) E D fxx(x, y) 0. elsewhere . where D is the region of the plane delimited by three lines: y = 1 (parallel to the r axes), x = 1 (parallel to the y axes), and y = 1- x. Determine 1. the marginal density of fx(x); 2. the conditional density of fY|x; 3. the independence (or dependence) between X and Y.
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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Answer all parts 1, 2, and 3 of the question below. Show all work and steps.
![Let \( X \) and \( Y \) be two random variables continuous with PDF equal to
\[
f_{X,Y}(x,y) =
\begin{cases}
2 & \text{if } (x, y) \in D \\
0 & \text{elsewhere}
\end{cases}
\]
where \( D \) is the region of the plane delimited by three lines: \( y = 1 \) (parallel to the \( x \)-axis), \( x = 1 \) (parallel to the \( y \)-axis), and \( y = 1 - x \). Determine:
1. the marginal density of \( f_X(x) \);
2. the conditional density of \( f_{Y|X} \);
3. the independence (or dependence) between \( X \) and \( Y \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F361779f5-7517-4850-b433-f5d42195c84d%2F89cde32c-b895-4a6b-9d23-4932fa6e1a7e%2F7y5yp3s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let \( X \) and \( Y \) be two random variables continuous with PDF equal to
\[
f_{X,Y}(x,y) =
\begin{cases}
2 & \text{if } (x, y) \in D \\
0 & \text{elsewhere}
\end{cases}
\]
where \( D \) is the region of the plane delimited by three lines: \( y = 1 \) (parallel to the \( x \)-axis), \( x = 1 \) (parallel to the \( y \)-axis), and \( y = 1 - x \). Determine:
1. the marginal density of \( f_X(x) \);
2. the conditional density of \( f_{Y|X} \);
3. the independence (or dependence) between \( X \) and \( Y \).
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