Let (X, Y) be a pair of jointly continuous random variables with joint density S{(* – y)°, (x,y) E [-1, 1)°, 10, f(x, y) otherwise (a) Compute the marginal density fx. (b) Set up an iterated integral to compute EY], but do not evaluate the integral.
Let (X, Y) be a pair of jointly continuous random variables with joint density S{(* – y)°, (x,y) E [-1, 1)°, 10, f(x, y) otherwise (a) Compute the marginal density fx. (b) Set up an iterated integral to compute EY], but do not evaluate the integral.
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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![Let \((X, Y)\) be a pair of jointly continuous random variables with joint density
\[
f(x, y) =
\begin{cases}
\frac{3}{8}(x-y)^2, & (x, y) \in [-1, 1]^2, \\
0, & \text{otherwise}
\end{cases}
\]
(a) Compute the marginal density \( f_X \).
(b) Set up an iterated integral to compute \( E[Y] \), but do not evaluate the integral.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fed3eef2a-70e8-485e-b91d-563de65921b3%2Fb8cb2a3f-4d3f-4794-bae8-1f8c20015e54%2Fcact2b6_processed.png&w=3840&q=75)
Transcribed Image Text:Let \((X, Y)\) be a pair of jointly continuous random variables with joint density
\[
f(x, y) =
\begin{cases}
\frac{3}{8}(x-y)^2, & (x, y) \in [-1, 1]^2, \\
0, & \text{otherwise}
\end{cases}
\]
(a) Compute the marginal density \( f_X \).
(b) Set up an iterated integral to compute \( E[Y] \), but do not evaluate the integral.
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