Fully formatted problems can be found in the attached Word document.

1) Let X have the p.d.f. f(x) = 4x^3 , 0<x<1

Find the p.d.f. of Y = X^2

2) Let x have a gamma distribution with =3 and  = 2

determine the p.d.f. of Y=X^2.

3) The P.d.f. of X is f(x) =  x^(-1), 0<x<1 , 0<<. Let Y=-2 lnX. How is Y distributed?

The solution introduces the Jacobian and how to apply it to solve each problem.