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这是名字 · 2025年06月22日

总体方差的无偏估计

NO.PZ2024120401000009

问题如下:

An experiment yields the following data:

It is hypothesized that the data come from a uniform distribution, U(0, b). What are the unbiased estimators of the mean and variance?

选项:

A.

0.39 0.08

B.

0.45 0.086

C.

0.39 0.086

D.

0.45 0.086

解释:

The sample mean is already unbiased:

For the variance:

这题用计算器算了一下,感觉想到个很奇怪的方式不知道对不对。用计算器可以计算出样本标准差和总体标准差。题目要求解总体方差的无偏估计,其实就是在求样本方差。所以直接用计算器的样本方差结果平方就可以了。这么理解对吗。

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