(Solution) - Consider X Y with joint density fX Y x y 1 2500 10 -(2025 Original AI-Free Solution)

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Consider X, Y with joint density
fX,Y(x, y) = 1/2500(10 - x)(10 -y),
for 0 ? x ? 10, 0 ? y ? 10,
and fxy(x,y) = 0 otherwise.
a. Find P(X < 9,y < 9).
b. Find P(X < 9,y > 9).
d. Find P(X > 9,Y > 9).
e. Check that the answers from parts a-d sum to 1. Exercise 11. Let X, Y have joint density