1. The problem statement, all variables and given/known data I am given the lens maker's equation: 1/u + 1/v = 1/f Then told that U and V are random variables based on this equation. U is uniformly distributed between 2f and 3f. The question is to prove the pdf of V is f/(v-f)^2 and find the cdf for V. Also - find the mean and mode of V. 2. Relevant equations 3. The attempt at a solution The PDF for U seems to be: f_u = U/f for U 2f < U < 3f (not they should be 'less than and equal etc.) f_u = 0 otherwise And the cumulative distribution seems to be F_U= 0 for U < 2f U-2f/f for 2f < U < 3f 1 for 3f < U Now my attempts to translate into V have failed. I tried the transformation u = fv/f-v but with no luck in getting any algebra that is meaningful. I realise that f is related to both u and v in a way that makes simple substitutions of probablity difficult to incorporate. Some help would be appreciated!