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.
\[p(X = x) =
\begin{cases}
\theta, x = 1\\
1 -\theta, x = 0
\end{cases}
\]
\[E(X) = \theta
\]
\[D(X) = \theta (1 - \theta)^2 + (1 - \theta)\theta^2 = \theta(1 - \theta)
\]
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.
\[E(Y) = E(X_1 + X_2 + \dots + X_n) = nE(X) = n\theta
\]
\[D(Y) = D(X_1 + X_2 + \dots + X_n) = nD(X) = n\theta(1 - \theta)
\]