Question: 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

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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