An ecologist wishes to mark off a circular sampling region having radius 12 m. However, the radius of the resulting region is actually a random variable R with the following pdf. f(r) = 41 [1 - (12 - )²] 11 ≤rs 13 0 otherwise What is the expected area of the resulting circular region? (Round your answer to two decimal places.) m²

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An ecologist wishes to mark off a circular sampling region having radius 12 m. However, the radius of the resulting region is actually a random variable R with the following pdf.
3
1- (12-)²]
√2 (1
4
f(r) =
0
m
11 ≤ ≤ 13
otherwise
What is the expected area of the resulting circular region? (Round your answer to two decimal places.)
2
Transcribed Image Text:An ecologist wishes to mark off a circular sampling region having radius 12 m. However, the radius of the resulting region is actually a random variable R with the following pdf. 3 1- (12-)²] √2 (1 4 f(r) = 0 m 11 ≤ ≤ 13 otherwise What is the expected area of the resulting circular region? (Round your answer to two decimal places.) 2
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