Question

An ecologist wishes to mark off a circular sampling region having radius 10 m. However, the radius of the resulting region is actually a random variable R with the following pdf.
f(r) = 3/4
1 − (14 − r)2
0
13 ≤ r ≤ 15

What is the expected area of the resulting circular region?

Answer 1

E(A)=E(πr^2)
=13 (upper limit of integral)
∫
15 (lower limit of integral)
πr^2 3 / 4[1−(14−r)^2]dr

integrating it would yield
981π / 5