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5897Overbetting to Twice KellyUnder the small-edge approximation G(f)\approx f-\tfrac12 2 f 2 for the expected log-growth of a repeated bet, the growth-optimal fraction is f *= / 2. At what (nonzero) betting fraction does the expected log-growth fall back to zero, and what does this say about the symmetry of growth around f *?概率中等数值题未尝试面试订阅5899Betting Kelly on the Wrong ProbabilityAn even-money coin truly wins with probability p=0.55, but you overestimate it as p=0.65 and bet the Kelly fraction implied by your estimate. What is your actual long-run expected log-growth rate per round? Compare it to the growth you would have earned betting the correct Kelly fraction, and state what the sign of your actual growth implies.概率困难数值题未尝试面试订阅