was asked this question today...you want buy a car at an auction whos price is uniformly distributed between 0-1000 if you bid more than the car you win it at the price you bid.if you bid less that the cars proce you dont win it but dont lose anything. you can sell the car for 1.5 time the value of which you bought it. what should you bid on the car to maximumise your profit?
i told the interviewer that the expected value is negitve so you should bid 0 to maximum your profit.(0 is greater that any negitive number) but the answer which i was guided towards wasE(X)= X-(X/2)*1.5 letting X = your bid so if you bid 500 E(x) = 500 - 250(1.5) = 125 pretty weird question if you ask me. comming up with a formula for expected value when i was orgionaly asked what would be my bid to maxiumise my profit. any1 have an thoughts? maybe this was obvious?
If you bid X then your expected gain is (X/2)*1.5 So (X/2)*1.5 - X should be your profit... I.E. negative expected value. Could it be the interview just wanted to see how you can mathematically back up your original statement?
yeah good point! that is most likely what he was testing. i suppose i just assumed it was obviously neg EV.
Apr 27, 2011