(X_1,X_2,cdots,X_n)为独立随机变量，且(X_i in [a,b]),随机变量的经验均值可表示为：
[overline{X}=frac{X_1+X_2+cdots+X_n}{n}
]
霍夫丁不等式叙述如下：
[(1)forall t >0, P(overline{X}-E(overline{X}) geqslant t) leqslant exp(-frac{2n^2t^2}{sum_{i=1}^{n}(b_i-a_i)^2})
]
[(2)forall t >0, P(E(overline{X})-overline{X} geqslant t) leqslant exp(-frac{2n^2t^2}{sum_{i=1}^{n}(b_i-a_i)^2})
]
[(3)forall t >0, P(|overline{X}-E(overline{X})| geqslant t) leqslant 2exp(-frac{2n^2t^2}{sum_{i=1}^{n}(b_i-a_i)^2})
]
令(S_n=X_1+X_2+cdots+X_n)
[(4)forall t >0, P(S_n-E(S_n) geqslant t) leqslant exp(-frac{2t^2}{sum_{i=1}^{n}(b_i-a_i)^2})
]
[(5)forall t >0, P(E(S_n)-S_n geqslant t) leqslant exp(-frac{2t^2}{sum_{i=1}^{n}(b_i-a_i)^2})
]
[(6)forall t >0, P(|S_n-E(S_n)| geqslant t) leqslant 2exp(-frac{2t^2}{sum_{i=1}^{n}(b_i-a_i)^2})
]