Let X and Y have joint PDF cy fxx(z,y) = { 0 0≤y≤z≤1 0 otherwise a) Draw the region of positive probability, and find constant c. b) Find fx(x) and fy (y). c) Find P[Y ≤X/2].
Let X and Y have joint PDF cy fxx(z,y) = { 0 0≤y≤z≤1 0 otherwise a) Draw the region of positive probability, and find constant c. b) Find fx(x) and fy (y). c) Find P[Y ≤X/2].
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![**Problem Statement: Joint Probability Density Function of \( X \) and \( Y \)**
Let \( X \) and \( Y \) have a joint PDF:
\[ f_{X,Y}(x,y) = \begin{cases}
cy & \text{if } 0 \le y \le x \le 1 \\
0 & \text{otherwise}
\end{cases} \]
**Questions:**
a) Draw the region of positive probability, and find constant \( c \).
b) Find \( f_X(x) \) and \( f_Y(y) \).
c) Find \( P[Y \le X/2] \).
d) Find \( E[X] \), \( E[Y] \), \(\sigma_X^2\), \(\sigma_Y^2\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F099a9854-7cc3-46b9-a37c-ec0486b4a12a%2Fc67ec3ca-5c7f-4f98-91bb-790bf3f8668a%2F3puk57g_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement: Joint Probability Density Function of \( X \) and \( Y \)**
Let \( X \) and \( Y \) have a joint PDF:
\[ f_{X,Y}(x,y) = \begin{cases}
cy & \text{if } 0 \le y \le x \le 1 \\
0 & \text{otherwise}
\end{cases} \]
**Questions:**
a) Draw the region of positive probability, and find constant \( c \).
b) Find \( f_X(x) \) and \( f_Y(y) \).
c) Find \( P[Y \le X/2] \).
d) Find \( E[X] \), \( E[Y] \), \(\sigma_X^2\), \(\sigma_Y^2\).
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