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Pdf of area and circumference of a circle

  • Thread starter uva123
  • Start date
  • #1
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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]r2
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
 

Answers and Replies

  • #2
lanedance
Homework Helper
3,304
2
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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