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Question: suppose that x and y are jointly continuous random variables...

Question details

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.

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