Suppose that the probability of success of one test is p, and 100 independent repeated tests are carried out=______ The standard deviation of success times is the largest, and the maximum value is______ ． | Math enthusiast | Mathematical art

Suppose that the probability of success of one test is p, and 100 independent repeated tests are carried out= The standard deviation of success times is the largest, and the maximum value is ．

From the variance formula of the independent repeated test, we can get D ξ = NPQ ≤ n (P + Q2) 2 = N4, the equal sign holds when p = q = 12, ∧ D ξ = 100 × 12 × 12 = 25, σ ξ = 25 = 5

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