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为了求职冲呀 · 2020年03月04日

问一道题:NO.PZ2015120604000053

问题如下:

According to Chebyshev’s Inequality, what is the minimum percentage of the observations from a positive skewed distribution that will be within ±3.5 standard deviations of the mean?

选项:

A.

8.2%.

B.

71.43%.

C.

91.8%.

解释:

C is correct

Chebyshev’s inequality states that regardless of the shape of the distribution, the percentage of the observations that lie within k standard deviations of the mean is at least 1-1/k2 for all k>1.

Applying Chebyshev’s inequality, 1 - [1 / (3.5)2] = 91.8%.

能不能麻烦老师讲下解题思路?

1 个答案

星星_品职助教 · 2020年03月04日

同学你好,

这道题题干中说明了要应用切比雪夫不等式,问的问题恰好是切比雪夫不等式描述的“对任何一组观测值,个体落在均值周围k个标准差之内的概率不小于1-1/k^2”,所以求这个最小的的percentage就直接代入公式即可,K=3.5,得到1 - [1 / (3.5)^2] = 91.8%