Problem 10. Let X and Y have joint density function f(x, y) = 1/y on the triangle 0 < x < y < 1.

a. Find the marginal probability density functions of X and Y .

b. Are X and Y independent?

c. Compute P(X + Y 1).

Problem 2. Let X be a uniform random variable on the interval (1, 1) and let Y = X2.

a. Find E(Y ).

b. Find the probability density function of Y .