The joint density of X and Y is given by f(x, y) = (1/2)y * e^(-xy), 0 < x < ∞, 0 < y < 2, and f(x, y) = 0 otherwise. Calculate E[e^(X/2)|Y = 1].
Added by Robert B.
Step 1
We can do this by dividing the joint density by the marginal density of Y. The marginal density of Y can be found by integrating the joint density with respect to x: f_Y(y) = \int_0^\infty f(x, y) dx = \int_0^\infty \frac{1}{2}ye^{-xy} dx To solve this Show more…
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