几何分布中样本X(n)和X(1)的概率分布:
P{X(n) ≤ k} = 1 - P{X(n) > k} = 1 - pqk
P{X(1) ≤ k} = 1 - P{X(1) > k} = 1 - (1 - p)k
正态分布样本的概率计算:
P{X̄(16) > 10} = 1 - Φ[(10 - 8) / √(4/16)] = 1 - Φ(1) = 0.9370
P{X̄(1) > 5} = Φ[(5 - 8) / √(4/1)] - Φ[(5 - 8) / √(4/16)] = 0.0933 - 0.0309 = 0.0624
韦布尔分布密度函数:
f(x) = (β / α)(x / α)^(β-1)exp[-(x / α)^β]