Consider two random variables X and Y with the following joint density function f(x,y) = {e^** a) Find marginal density function of Y. b) Find f(x| Y = 2) c) Find F(x|Y) 0 ≤ y ≤x<∞0 elsewhere
Consider two random variables X and Y with the following joint density function f(x,y) = {e^** a) Find marginal density function of Y. b) Find f(x| Y = 2) c) Find F(x|Y) 0 ≤ y ≤x<∞0 elsewhere
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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![Consider two random variables \( X \) and \( Y \) with the following joint density function:
\[
f(x, y) =
\begin{cases}
e^{-x}, & 0 \leq y \leq x < \infty \\
0, & \text{elsewhere}
\end{cases}
\]
Tasks:
a) Find the marginal density function of \( Y \).
b) Find \( f(x | Y = 2) \).
c) Find \( F(x | Y) \).
d) Find \( P(X - Y \geq 1) \).
e) Find \( P(Y = 2) \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F197e26df-0092-4237-9a65-d284350ca22d%2F7d9db361-3063-44c2-9464-9ee2b0611b40%2Fiif49i_processed.png&w=3840&q=75)
Transcribed Image Text:Consider two random variables \( X \) and \( Y \) with the following joint density function:
\[
f(x, y) =
\begin{cases}
e^{-x}, & 0 \leq y \leq x < \infty \\
0, & \text{elsewhere}
\end{cases}
\]
Tasks:
a) Find the marginal density function of \( Y \).
b) Find \( f(x | Y = 2) \).
c) Find \( F(x | Y) \).
d) Find \( P(X - Y \geq 1) \).
e) Find \( P(Y = 2) \).
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