概率论,高数微积分.为什么是几何分布

2025-03-31 19:16:02
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概率论,高数微积分.为什么是几何分布
设 P(X[1]) = p.则,
P(X[2]) = (1/3)P(X[1]) = (1/3^2)p,.
P(X[1]) +P(X[2])+P(X[3])+.= p+(1/3)p+(1/3^2)p+...=p/(1-(1/3)) =1 --> p=2/3
P(X[1]) = 2/3
P(X[2]) = (1/3)(2/3)
P(X[3]) = (1/3^2)(2/3)
P(X[n]) = (1/3^(n-1))(2/3)