Expected winning and second-highest bid in an auction
Asked at Jane Street
An item draws independent bids, each uniform on (measured as a fraction of the item's max value).
What is the expected highest bid, and the expected second-highest bid? Apply both to .
Show a hint
The highest bid is the max of the draws; the second-highest is the next order statistic down. Each uniform order statistic has a clean expected value.
Your answer
This one is open-ended. Work it through, then check your reasoning against the full solution.