Question

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(n) = 1 - 2 115rs 13 otherwise What is the expected area of the resulting circular region? (Round your answer to two decimal places.) 453.20 x m2

Answer 1

TOPIC:Expected value of random variables.

= The bold of madrus (R) a given as den) [(1-3); s otherwise. n we have E (R) - 1 r Jea) din - - [i-1-99 s. *** [-(--> 3). *E** 24- 25 143 2 3 713 + 24

2.1435 +66 . (10) - 6+60196-2.1 144.20. so, & (R²) = 144. 20, Now the circle. A = Area of STR. i we need, = E(A). = E(AR²). X. E (R²) = A x 144.20.

= 144.20 x ā. a 144.20 x 3. 14 159. I d Exact I value of = 3.1415 9 = 453.017278 m². 453. 02/ (rounded to a two decimals