4.6-1.ppt - 概率论与数理统计是研究随机现象统 计规律性的学科 随机现象的规律性只有

# 4.6-1.ppt -...

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4.6.1 切比雪夫不等式 设随机变量 X 有期望 E ( X ) 和方差 ，则对于 任给 >0, 2 由切比雪夫不等式可以看出，若 越小，则事件 {| X - E ( X )|< } 的概率越大 ，即随机变量 X 集中在期望附近的可能 性越大 . 2 2 2 1 } | ) ( {| X E X P 2 2 } | ) ( {| X E X P 由此可体会方差的概率意义： 它刻划了随机变量取值的离散程度 .

1: 已知正常男性成人血液中，每一毫 升白细胞数平均是 7300 ，均方差是 700 . 利用切比雪夫不等式估计每毫升白细胞数 5200~9400 之间的概率 . 解：设每毫升白细胞数为 X 依题意， E ( X )=7300, D ( X )=700 2 所求为 P (5200 X 9400)
P(5200 X 9400) = P (5200- 7300 X - 7300 9400- 7300 ) = P (-2100 X - E ( X ) 2100) 2 ) 2100 ( ) ( 1 X D = P { | X - E ( X )| 2100} 由切比雪夫不等式 P { | X - E ( X )| 2100} 2 ) 2100 700 ( 1 9 8 9 1 1

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