数学试题讲解

设

X_{1}, X_{2}, X_{3}

相互独立且

E (X_{i}) = 1, D (X_{i}) = 1 (i = 1, 2, 3)

, 则对于任意给定的

ε > 0

由切比雪夫不等式可得

P (| \sum_{i = 1}^{3} X_{i} - 1 | < ε) \geq 1 - ε^{- 2}

P (| \frac{1}{3} \sum_{i = 1}^{3} X_{i} - 1 | < ε) \geq 1 - ε^{- 2}

P (| \sum_{i = 1}^{3} X_{i} - 3 | < ε) \geq 1 - ε^{- 2}

P (| \sum_{i = 1}^{3} X_{i} - 3 | < ε) \geq 1 - 3 ε^{- 2}