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 pdf What is the expected area of the resulting circular region?

Answer Step 1 of 2 11 11 3 2 E(r)= rf(r) dr = 4(1 (10 r )) dr 9 9 11 3r 2 = 4 (r 9) dr 9 4 2 11 = 3 r 9r 4 [ 43 2 ]9 3 114 9(11 ) 94 9(9 ) = 4( 4 2 ) (4 2 )} 3 7361 = 4 4 )=1380.18