Bernoulli Experiment, Bernoulli Distribution, 0-1 Distribution
最常见的伯努利试验是抛一次硬币. 伯努利试验的结果服从伯努利分布: 随机变量只可能取0, 1两个值, 所以也称0-1分布.
[p(X = x) =
egin{cases}
heta, x = 1\
1 - heta, x = 0
end{cases}
]
[E(X) = heta
]
[D(X) = heta (1 - heta)^2 + (1 - heta) heta^2 = heta(1 - heta)
]
二项式分布, Binomial Distribution
(n)次独立的伯努利试验的结果服从二项式分布.
[E(Y) = E(X_1 + X_2 + dots + X_n) = nE(X) = n heta
]
[D(Y) = D(X_1 + X_2 + dots + X_n) = nD(X) = n heta(1 - heta)
]