Consider X, Y with joint density fX,Y(x, y) = 1/2500(10 - x)(10 -y), for 0 x

Question:

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).
c. Find P(X > 9,Y > 9).
d. Check that the answers from parts a-d sum to 1. Exercise 11. Let X, Y have joint density