Exercise 6.55 Let X and Y be random variables with joint density function if x, y > 0, f (x, y) = otherwise. Show that the joint density function of U = (X – Y) and V = Y is te -u-v if (u, v) E A, fu,v (u, v) = otherwise, where A is a region of the (u, v) plane to be determined. Deduce that U has the bilateral exponential distribution with density function fu (u) = ¿e-lu| for u e R.

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Exercise 6.55 Let X and Y be random variables with joint density function
if x, y > 0,
f (x, y) =
otherwise.
Show that the joint density function of U = (X – Y) and V = Y is
te
-u-v
if (u, v) E A,
fu,v (u, v) =
otherwise,
where A is a region of the (u, v) plane to be determined. Deduce that U has the bilateral exponential
distribution with density function
fu (u) = ¿e-lu|
for u e R.
Transcribed Image Text:Exercise 6.55 Let X and Y be random variables with joint density function if x, y > 0, f (x, y) = otherwise. Show that the joint density function of U = (X – Y) and V = Y is te -u-v if (u, v) E A, fu,v (u, v) = otherwise, where A is a region of the (u, v) plane to be determined. Deduce that U has the bilateral exponential distribution with density function fu (u) = ¿e-lu| for u e R.
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