Question

5. The Department of Energy (DOE) puts projects out on bid and generally estimates what a reasonable bid should be. Let b be the preliminary estimate of the bid. The DOE has determined that the density function of the winning bid is f(x) = {8} if şb sxs 2b elsewhere i. Verify that f(x) is a valid probability density functio ii. Find the cumulative distribution function, F(x). iii. Use the results in part Q4 b(ii) to determine the probability that winning bid is greater than the DOE's preliminary estimate.

Answer 1

Page No. Date & Given density function. 7x)= f i t b 285 2b To ; elsewhere Cheching the validity rig 2b 5 dxz S 8b 215b 215b 5 [2b - 2b Yes, it is a valid pdf u Cumulative distribution function f (x). Fx (x) =P [X 2x] = 5 at 2 2 z b x - 27 . 2/5 b (1) ELх- - Fx (x) = S(x - 215 6] 2- 215b