(adsbygoogle = window.adsbygoogle || []).push({}); 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=[tex]\Pi[/tex]r^{2}

Circumference=2[tex]\Pi[/tex]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))={[tex]\Pi[/tex][(1/8)(3x+1)]^{2}for 0<x<2

0 otherwise

likewise for circumference

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

**Physics Forums | Science Articles, Homework Help, Discussion**