Say we have a random variable A and the only thing we know about it, is that it is non-negative. Then we have another random variable B, which is a function of A. B = ln A. Say we know the PDF of A, described as 1/4 in case 2 < a <= 6, and 0 in every other case. We don't know the precise PDF of B, but we know that in accordance to the PDF of A, the limits of values for B is ln(2) < b <= ln(6). Now we'd like to have a value for g(b), as part of the PDF. It is not the same as the equivalent in A, where it is 1/4. What is it instead