# Question: Let X have a uniform distribution on the interval 0 1

Let X have a uniform distribution on the interval (0,1). Given that X = x, let Y have a uniform distribution on the interval (0, x + 1).

(a) Find the joint pdf of X and Y. Sketch the region where f(x, y) > 0.

(b) Find E(Y | x), the conditional mean of Y, given that X = x. Draw this line on the region sketched in part (a).

(c) Find fY(y), the marginal pdf of Y. Be sure to include the domain.

(a) Find the joint pdf of X and Y. Sketch the region where f(x, y) > 0.

(b) Find E(Y | x), the conditional mean of Y, given that X = x. Draw this line on the region sketched in part (a).

(c) Find fY(y), the marginal pdf of Y. Be sure to include the domain.

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