4.2.ppt - 4.2 随机变量的方差 上一讲我们介绍了随机变量的数学 期望,它体现了随机变量取值的平均水平

4.2.ppt - 4.2 随机变量的方差...

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上一讲我们介绍了随机变量的数学 期望,它体现了随机变量取值的平均水平 ,是随机变量的一个重要的数字特征 . 但是在一些场合,仅仅知道平均值是 不够的 . 4.2 随机变量的方差
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例如,某零件的真实长度为 a ,现用 甲、乙两台仪器各测量 10 次,将测量结果 X 用坐标上的点表示如图: 若让你就上述结果评价一下两台仪器的 优劣,你认为哪台仪器好一些呢? a 乙仪器测量结果 a 甲仪器测量结果 较好 测量结果的 均值都是 a 因为乙仪器的测量结果集中在均值附近
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又如 , 甲、乙两门炮同时向一目标射击 10 炮弹,其落点距目标的位置如图: 你认为哪门炮射击效果好一些呢 ? 甲炮射击结果 乙炮射击结果 乙炮 因为乙炮的弹着点较集中在中心附近 . 中心 中心
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为此需要引进另一个数字特征 , 它来度量随机变量取值在其中心附近的 离散程度 . 这个数字特征就是我们这一讲要介绍的 方差
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一、方差的定义 采用平方是为了保证一切 差值 X - E ( X ) 都起正面的作用 由于它与 X 具有相同的度量单位,在 实际问题中经常使用 .
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