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薛真 · 2021年04月10日

样本方差不是除以N-1吗,怎么除了N

NO.PZ2020010304000035

问题如下:

An experiment yields the following data:

It is hypothesized that the data comes from a uniform ditribution, U(0, b).

a. Calculate the sample mean and variance.

b. What are the unbiased estimators of the mean and variance?

c. Calculate the b in U(0, b) using the formula for the mean of a uniform distribution and the value of the unbiased sample mean found in part b.

d. Calculate the b in U(0, b) using the formula for the variance of a uniform distribution and the value of the unbiased sample variance found in part b.

选项:

解释:

a. Use the standard formual to get the sample variance(here, n=15)

μ=n1i=1nXi=0.39\mu = n^{-1}\sum_{i=1}^{n}X_i =0.39

σ2=n1i=1n(Xiμ)2=0.08\sigma^2 = n^{-1}\sum_{i=1}^{n}{(X_i-\mu)}^2 =0.08

b.The sample mean is already unbiased.

For the variance:

s2=nσ2/(n1)=150.080/14=0.086s^2=n\sigma^2/(n-1) =15*0.080/14=0.086

c.The mean for a U(a,b) distribution is given as:

μ=(a+b)/2

0.385=(0+b)/2

b=0.77

d. The variance for a U(a,b) distribution is given as:

σ2=(ba)2/12\sigma^2=(b-a)^2/12

0.086=b2/120.086=b^2/12

b=1.016b=1.016

样本方差不是除以N-1吗,怎么除了N

1 个答案

品职答疑小助手雍 · 2021年04月10日

嗨,从没放弃的小努力你好:


计算无偏估计的样本方差的时候是第二步里面的,用第一步的结果乘以n再除以n-1。

第一步它算的样本variance是有偏的。考试不会出这么细的啦,问样本方差的话直接除以n-1就好。(其实也很少直接考方差的计算的)

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