Problem 9: Random variables X and Y have the joint PDF S c(2 – 2), 1<* < 2, 0 < y < 2, 0, Sx.y(x, y) otherwise. (a) Find the constant c.
Problem 9: Random variables X and Y have the joint PDF S c(2 – 2), 1<* < 2, 0 < y < 2, 0, Sx.y(x, y) otherwise. (a) Find the constant c.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
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 9:** Random variables \( X \) and \( Y \) have the joint PDF
\[
f_{X,Y}(x, y) =
\begin{cases}
c(2-x), & 1 \leq x \leq 2, \, 0 \leq y \leq 2, \\
0, & \text{otherwise}.
\end{cases}
\]
**(a)** Find the constant \( c \).
**(b)** Find the marginal PDF \( f_X(x) \).
**(c)** Let \( U = g(X) = \sqrt{X} \). Find the PDF of \( U \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbddf1426-a28f-4b9c-96ed-ee115a37a4b2%2Fc5f2cdef-d987-48d2-90da-59e24306a72b%2Fvgn3bpg_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 9:** Random variables \( X \) and \( Y \) have the joint PDF
\[
f_{X,Y}(x, y) =
\begin{cases}
c(2-x), & 1 \leq x \leq 2, \, 0 \leq y \leq 2, \\
0, & \text{otherwise}.
\end{cases}
\]
**(a)** Find the constant \( c \).
**(b)** Find the marginal PDF \( f_X(x) \).
**(c)** Let \( U = g(X) = \sqrt{X} \). Find the PDF of \( U \).
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