Mathematics, 29.07.2020 04:01 savannabroyhill24
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)={34(1−(14−r)2)13≤r≤150 otherwise
What is the expected area of the resulting circular region?
Answers: 2
otherwise
![E(r^2) = \dfrac{3}{4}[\dfrac{28 r^4}{4}-\dfrac{r^5}{5}-\dfrac{195r^3}{3}]^{^{15}}}__{13}](/tpl/images/0714/5743/76310.png)
![E(r^2) = \dfrac{3}{4} [ \dfrac{28 \times 50625}{4} - \dfrac{759375}{5} - \dfrac{195 \times 3375}{3} ]-[ \dfrac{28 \times 28561}{4} - \dfrac{371293}{5} - \dfrac{195 \times 2197}{3} ]](/tpl/images/0714/5743/4623b.png)
![E(r^2) = \dfrac{3}{4} [ 354375-151875-219375-199927+74258.6+142805]](/tpl/images/0714/5743/58232.png)
![E(r^2) = \dfrac{3}{4} [261.6]](/tpl/images/0714/5743/ac5ac.png)
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