In Exercises 117 and 118, as well as many other situations, one has the pdf f(x) of X and wishes to know the pdf of y = h(X). Assume that h( ? ) is an invertible function, so that y= h(x) can be solved for x to yield x = k(y). Then it can be shown that the pdf of Y is
a. If X has a uniform distribution with A = 0 and B = 1, derive the pdf of Y = 2ln(X).
b. Work Exercise 117, using this result.
c. Work Exercise 118(b), using this result.