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. 1- (10-)²] 9 ≤r≤ 11 0 otherwise 3 [₁ f(r) = 4 What is the expected area of the resulting circular region? (Round your answer to two decimal places.) m²

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.3: Special Probability Density Functions
Problem 26E
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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)
4
m
-
(10 - r)²] 9 < r ≤ 11
0
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 10 m. However, the radius of the resulting region is actually a random variable R with the following pdf. f(r) 4 m - (10 - r)²] 9 < r ≤ 11 0 otherwise What is the expected area of the resulting circular region? (Round your answer to two decimal places.) 2
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