If x and y are independent continuous positive random
variables, express the density function of (a) z=x/y and (b) z=xy in
terms ofthe density functions of x and y. evaluate these
expressions in thespecial case where x and y are both exponential
randomvariables.

a) has CDF

where the last equality follows from independence of . In terms of the distribution and density functions of , this is

Then the density is obtained by differentiating with respect to ,

b) can be computed in the same way; it has CDF

Differentiating gives the associated PDF,

Assuming and , we have

and

I wouldn't worry about evaluating this integral any further unless you know about the Bessel functions.

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