(a) Show that the joint pdf for U, V is of the form f(x, y) = { exp(-u-v), if (u, v) E A otherwise %3D 0. where A is a subset of the (u, v) plane that you should determine. (b) Find the marginal pdf of U.

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Let X and Y be random variables with joint pdf
f (r, v) = {
texp(-을(z + y), if z > 0,y > 0
otherwise
Let
U =
(X-Y),
V =Y
(a) Show that the joint pdf for U, V is of the form
f(z, y) = {2 exp(-u-v), if (u, v) EA
otherwise
%3D
where A is a subset of the (u, v) plane that you should determine.
* (b) Find the marginal pdf of U.
Transcribed Image Text:Let X and Y be random variables with joint pdf f (r, v) = { texp(-을(z + y), if z > 0,y > 0 otherwise Let U = (X-Y), V =Y (a) Show that the joint pdf for U, V is of the form f(z, y) = {2 exp(-u-v), if (u, v) EA otherwise %3D where A is a subset of the (u, v) plane that you should determine. * (b) Find the marginal pdf of U.
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