hard · Quantitative Finance quant-logic
You will be shown a sequence of n=100 distinct numbers one at a time in random order. After seeing each, you must immediately accept (stop) or reject (continue) it; you cannot return to a rejected number. You win only if you stop on the single largest of all 100.
Using the optimal strategy (reject the first r-1, then take the first number exceeding all seen so far), the optimal threshold r and resulting win probability P^* satisfy which statement?
- r≈ 50 and P^*≈ 1/2, since you should reject the first half.
- r≈ 37 and P^*≈ 0.371, both approaching 1/e for large n.
- r≈ 37 but P^*≈ 0.01, since exactly one of 100 is the max.
- r≈ 63 and P^*≈ 1-1/e≈ 0.632.
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