Question: 1. If X and Y are independent random variables with density functions fX and fY , respectively, show that U = XY and V =

1. If X and Y are independent random variables with density functions fX and fY , respectively, show that U = XY and V = X/Y have density functions fU (u) =

∞

−∞

fX (x) fY (u/x)

|x|

dx, fV (v) =

∞

−∞

fX (vy) fY (y)|y| dy.

2. Is the function G, defined by G(x, y) =

(

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