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?

Question

Brody Wood

Mathematics

6 May, 10:12

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?

+4

Answers (1)

Know the Answer?

Roland Patterson · Answer 1

E (A) = E (π r^2)

=13 (upper limit of integral)

∫

15 (lower limit of integral)

π r^2 3 / 4 [1 - (14-r) ^2 ]dr

integrating it would yield

981π / 5

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) = 3/41 - (14 - r) 2013 ≤ r ≤ 15What is the expected area of the resulting circular region?

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?