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 ? (12 ? r)^2] 11 ? r ? 13 0 otherwise

What is the expected area of the resulting circular region? (Round your answer to two decimal places.)

Answer 1

expected area = 453.20 m^2

Explanation:

The given data 11 ≤ r ≤ 13

`\left \{ {{3/4(1-(12-r)^2} \atop {0}} \right.` o / w

Th expected area of the insulating circular region can be calculated using

= E(
`\pi r^2 )`

=
`\pi E(r^2)`

we will have to calculate
`E(r^2)`

attached is the remaining part of the solution