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mario62 [17]
3 years ago
14

An ecologist wishes to mark off a circular sampling region having radius 10 m. However, the radius of the resulting region is ac

tually 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.)

Mathematics
1 answer:
ehidna [41]3 years ago
3 0

Answer:

expected area = 453.20 m^2

Step-by-step 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

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