medium Probability

Optimal Bidders I

A release-checked medium problem for training Expected Value, Continuous Random Variables.

Question

Carter has come into contact with a bounty of gold. He takes it to an auction shop. The auction shop says that each person that bids will place a bid that is uniformly distributed between $\$500$ and $\$1000$. They also state that they can recruit people to bid for a price of $\$5$ per person. Assuming Carter selects the optimal number of people to bid on his gold, what is his expected payout?

Practice focus

This Probability problem is tagged Expected Value, Continuous Random Variables. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.