The joint density of the bivariate random variable ((X, Y)) is given by (f(x, y)=x y I_{[0,1]}(x)

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The joint density of the bivariate random variable $(X, Y)$ is given by

$f(x, y)=x y I_{[0,1]}(x) I_{[0,2]}(y)$.

a. Find the joint cumulative distribution function of $(X, Y)$. Use it to find the probability that $x \leq .5$ and $y \leq 1$.

b. Find the marginal cumulative distribution function of $X$. What is the probability that $x \leq .5$ ?

c. Find the marginal density of $X$ from the marginal cumulative distribution of $X$.

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Mathematical Statistics For Economics And Business

ISBN: 9781461450221

2nd Edition

Authors: Ron C.Mittelhammer

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Question Posted: Feb 28, 2024 02:01 AM

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The joint density of the bivariate random variable ((X, Y)) is given by (f(x, y)=x y I_{[0,1]}(x)

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Mathematical Statistics For Economics And Business

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