Question

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-((15-r)^2)) 14≤r≤16
0 otherwise

What is the expected area of the resulting circular region? (Round your answer to two decimal places.)

Answer 1

Is this what you're asking? \[f(r)=\frac{3}{4}(1-(15-r)^{2}),14\le r\le16\]

Answer 2

Yes

Answer 3

Okay. So you have the radius value already, r=10, yes?

Answer 4

oh yes

Answer 5

I believe you just need to input that value for r in the equation.
Though if it's not, then I'm not sure. I haven't done Stats in awhile haha ^-^;

Answer 6

I tried to put it into the equation twice but it was wrong and I've got the last chance to check answer.....

Answer 7

Hrm... well, you can always check answers with Mathway - http://www.mathway.com/
Cymath is also a good site to run through the steps - http://www.cymath.com/

(there's also WolframAlpha but idk if that will help much as of now)

Answer 8

Oh Thanks for the help :)

Answer 9

Yeah, sorry > <
I'm not too hot at Stats now. I need to fix that ahah
@hartnn or @Directrix should be able to help maybe though, they're math pros ☺

Answer 10

@satellite73

Answer 11

Its asking to the expected value of the pdf. i think

Answer 12

\[\mathbb{E}[x] = \int_{-\infty}^\infty xf(x) dx\]

Answer 13

@kittiwitti1

Look at @Zarkon 's work here:

http://openstudy.com/study#/updates/4f616c8ee4b079c5c630f224

Answer 14

Ah... I haven't done statistics of that advanced level. It was really just a mini introductory run-through ^-^; @Directrix
My apologies @kim3584 I was not experienced enough to help you :(

Answer 15

@kim3584

Answer 16

Oh I saw that already.
I did not try yet so I will try it.
Thanks.