Painting I

What this optimal-bidding interview question tests

This is an easy statistics and decision theory question that asks you to find the bid that maximizes expected profit under uncertainty. It's a classic auction and valuation problem that tests whether you can set up an optimization problem from first principles and reason about payoffs across different scenarios.

To solve it, you need to recognize that your profit depends on whether your bid exceeds the true value, and then express expected profit as a function of your bid. The key insight is understanding how the uniform distribution of the painting's value interacts with your win condition and payout structure. Strong solutions explicitly write down the expected-value formula, differentiate or reason about it algebraically, and verify that the resulting bid is sensible given the constraints.

• Expected value under uncertainty
• Payoff functions and win/loss conditions
• Optimization and marginal reasoning