Consider the following joint density (with support shown in the graph): 3 f(y1, Y2) : 91, 41, 0< y1, 0< y2; Y1 + Y2 < 3, 0, else. 1 Find the marginal densities f1(y1) and f2(y2) and the conditional density f(yı|42). Calculate Cov(Yı, Y2). 0 1 2 3 1;
Consider the following joint density (with support shown in the graph): 3 f(y1, Y2) : 91, 41, 0< y1, 0< y2; Y1 + Y2 < 3, 0, else. 1 Find the marginal densities f1(y1) and f2(y2) and the conditional density f(yı|42). Calculate Cov(Yı, Y2). 0 1 2 3 1;
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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![**Consider the following joint density (with support shown in the graph):**
\[ f(y_1, y_2) = \begin{cases}
\frac{2}{9} y_1, & 0 \leq y_1, \ 0 \leq y_2, \ y_1 + y_2 \leq 3, \\
0, & \text{else.}
\end{cases} \]
Find the marginal densities \( f_1(y_1) \) and \( f_2(y_2) \) and the conditional density \( f(y_1|y_2) \). Calculate \(\text{Cov}(Y_1,Y_2)\).
**Graph Detail:**
The graph displays a triangle in the coordinate plane with vertices at (0,0), (3,0), and (0,3). This triangle represents the support of the joint density function, where both \( y_1 \) and \( y_2 \) are non-negative and their sum does not exceed 3.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd25862a1-37f9-4b5c-af12-2fcd148d19b2%2F80d4868a-5140-4215-8f50-6dbf63d724ae%2F36vyp1a_processed.png&w=3840&q=75)
Transcribed Image Text:**Consider the following joint density (with support shown in the graph):**
\[ f(y_1, y_2) = \begin{cases}
\frac{2}{9} y_1, & 0 \leq y_1, \ 0 \leq y_2, \ y_1 + y_2 \leq 3, \\
0, & \text{else.}
\end{cases} \]
Find the marginal densities \( f_1(y_1) \) and \( f_2(y_2) \) and the conditional density \( f(y_1|y_2) \). Calculate \(\text{Cov}(Y_1,Y_2)\).
**Graph Detail:**
The graph displays a triangle in the coordinate plane with vertices at (0,0), (3,0), and (0,3). This triangle represents the support of the joint density function, where both \( y_1 \) and \( y_2 \) are non-negative and their sum does not exceed 3.
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