Question

Suppose that X and Y are jointly continuous random variables with joint density
f(x, y) = (
ye−xy 0 < x < ∞, 1 < y < 2
0 otherwise
(a) Given that X > 1, what is the expected value of Y ? That is, calculate E[Y | X > 1].
(b) Given that X > Y , what is the expected value of X? For this part, you are only required
to set up the requisite integrals, but not required to evaluate them.
(c) Compute E[X | Y ].

6. Suppose that X and Y are jointly continuous random variables with joint density f(z,y,-10 otherwise (a) Given that X 1, what is the expected value of Y? That is, calculate EY | X>1]. (b) Given that X > Y, what is the expected value of X? For this part, you are only required to set up the requisite integrals, but not required to evaluate them (c) Compute EX Y.

Answer 1

2. y et d 1 2. -1 (b) E [x/x

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