Question

PROB&STAT ANYONE!!

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 − (14 − r)2
0
13 ≤ r ≤ 15 otherwise

What is the expected area of the resulting circular region?

Answer 1

is this your pdf

\[f_{R}(r)=\left\{\begin{matrix}\frac{3}{4}[1-(14-r)^2] & \text{if }13\le r\le 15 \\ 0 & \text{o.w.}\end{matrix}\right.\]

Answer 2

yes it is :)

Answer 3

\[\mathbb{E}(A)=\mathbb{E}(\pi r^2)=\int\limits_{13}^{15}\pi r^2\frac{3}{4}[1-(14-r)^2]dr\]

Answer 4

how do i get an answer from that

Answer 5

you integrate it...\[\frac{981\pi}{5}\]

Answer 6

do i put that in a calculator

Answer 7

you could have your calculator integrate it...you can also expand the integrand and integrate term by term.

Answer 8

i got it! Thank you so much , i really appreciate u checking out my question

Answer 9

no problem