# Homework Help: Statistics - related pdfs

1. Feb 11, 2010

### Ferrus

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!

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