- #1

- 9

- 0

## Homework Statement

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.

## Homework Equations

Area=[tex]\Pi[/tex]r

^{2}

Circumference=2[tex]\Pi[/tex]r

## 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))={[tex]\Pi[/tex][(1/8)(3x+1)]

^{2}for 0<x<2

0 otherwise

likewise for circumference