Question: Show that the joint probability density function of U = 1 2 (X Y) and V = Y is fU,V (u, v) = (

Show that the joint probability density function of U = 1 2 (X − Y) and V = Y is fU,V (u, v) =

(

1 2 e−u−v if (u, v) ∈ A, 0 otherwise, where A is a region of the (u, v) plane to be determined. Deduce that U has probability density function fU(u) = 1 2 e−|u|, −∞ < u < ∞.

(Oxford 2008)

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