# Homework Help: Pdf of area and circumference of a circle

1. May 10, 2010

### uva123

1. The problem statement, all variables and given/known data
Suppose that the radius X of a circle is a random variable having the following p.d.f.:
f(x)={ (1/8)(3x=1) for 0<x<2
0 otherwise
Determine the p.d.f. of the area of the circle and the circumference of the circle.
2. Relevant equations
Area=$$\Pi$$r2
Circumference=2$$\Pi$$r
3. The attempt at a solution
can i just insert f(x) in for r in both equations to generate the pdf??
meaning....
if g is the area of the circle with r=f(x)
g(f(x))={$$\Pi$$[(1/8)(3x+1)]2 for 0<x<2
0 otherwise
likewise for circumference

2. May 10, 2010

### lanedance

no, they will be related by
$$|f(r)dr| = |f(c)dc|$$

where c is circumference & teh change dc correspond to the incremental dr