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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
    Area=[tex]\Pi[/tex]r2
    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
     
  2. jcsd
  3. May 10, 2010 #2

    lanedance

    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
     
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