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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.)

Respuesta :

batolisis

Answer:

expected area = 453.20 m^2

Step-by-step explanation:

The given data     11 ≤ r ≤ 13

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

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

= E([tex]\pi r^2 )[/tex]

= [tex]\pi E(r^2)[/tex]

we will have to calculate  [tex]E(r^2)[/tex]

attached is the remaining part of the solution

Ver imagen batolisis

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