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Roll 5 fair dice and take the maximum. What's the expected value? Most people say somewhere between 4 and 5, maybe guess 4.5. The actual answer is about 4.96, and the gap between intuition and reality is exactly why quant interviewers love these problems.
Wait, let's be precise about that. The expected maximum of 5 rolls of a fair six-sided die is:
$$E[X_{(5)}] = \sum_{k=1}^{6} k \cdot P(X_{...
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