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Elsa陆艳 · 2022年01月09日

可以完整的讲一下这个题吗?

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

看不太明白

1 个答案
已采纳答案

品职答疑小助手雍 · 2022年01月10日

同学你好,第一问均值就是15个值的平均数,方差就是每个数字减平均数得到的值平方之后的合再除以15。

第二问,只有这一个样本,那均值就是无偏估计的,方差要变成样本方差才是无偏估计的,公式是第一问求出的平方的合除以(15-1)。

第三问,均匀分布的均值第一问求出来了,下限a=0,套用均匀分布的均值公式求上限b即可。

第四问,同样的已知均匀分布的样本方差,和a,套用公式求剩下唯一一个未知数b。

以上公式在均匀分布部分的讲义里都有。


另外,我觉得你不太可能不会算均值,总体方差和样本方差这些概念,因此提问时候建议针对自己不会的地方进行提问。

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