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Medium · Probability & Statistics · Quant Trader interview question · probability, expected-value, permutation, fixed-point
Imagine you are a clerk at a hat check. You have $n$ hats and $n$ owners. Due to your lack of focus, you return the hats randomly to the owners. A "fixed point" is when an owner receives their own hat. What is the expected number of owners who receive their own hat (fixed points)?