Let X and Y have the joint density f (x, y) = 6 7 (x +
Chapter , Problem 8(choose chapter or problem)
Let X and Y have the joint density
\(f(x, y)=\frac{6}{7}(x+y)^{2}\), \(\quad 0 \leq x \leq 1\), \(\quad 0 \leq y \leq 1\)
a. By integrating over the appropriate regions, find (i) P(X > Y), (ii) \(P(X+Y \leq 1)\), (iii) \(P(X\leq \frac{1}{2})\).
b.Find the marginal densities of X and Y.
c.Find the two conditional densities.
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