- #1
uva123
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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