1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
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

  1. May 10, 2010 #1
    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
    3. The attempt at a solution
    can i just insert f(x) in for r in both equations to generate the pdf??
    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
  2. jcsd
  3. May 10, 2010 #2


    User Avatar
    Homework Helper

    no, they will be related by
    [tex] |f(r)dr| = |f(c)dc| [/tex]

    where c is circumference & teh change dc correspond to the incremental dr
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook