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ARIAZHU · 2021年11月15日

d 选项的答案为什么要除以12 ?

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

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

σ

2

=

(

b

a

)

2

/

12

σ2

=(b−a)2

/12

0.086

=

b

2

/

12

0.086=b2

/12

b

=

1.016

b=1.016

1 个答案

品职答疑小助手雍 · 2021年11月16日

同学你好,这个是直接套的基础班讲义88页均匀分布的方差公式,这个方差公式记住就好了,推论过程没在考纲范围内。

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NO.PZ2020010304000035问题如下experiment yiel the following tIt is hypothesizeththe ta comes from a uniform tribution, U(0, b). Calculate the sample meanvariance. Whare the unbiaseestimators of the meanvariance?Calculate the b in U(0, using the formula for the meof a uniform stribution anthe value of the unbiasesample mefounin part b. Calculate the b in U(0, using the formula for the varianof a uniform stribution anthe value of the unbiasesample varianfounin part b.Use the stanrformuto get the sample variance(here, n=15)μ=n−1∑i=1nXi=0.39\mu = n^{-1}\sum_{i=1}^{n}X_i =0.39μ=n−1∑i=1n​Xi​=0.39σ2=n−1∑i=1n(Xi−μ)2=0.08\sigma^2 = n^{-1}\sum_{i=1}^{n}{(X_i-\mu)}^2 =0.08σ2=n−1∑i=1n​(Xi​−μ)2=0.08b.The sample meis alrea unbiaseFor the variance:s2=nσ2/(n−1)=15∗0.080/14=0.086s^2=n\sigma^2/(n-1) =15*0.080/14=0.086s2=nσ2/(n−1)=15∗0.080/14=0.086c.The mefor a U(a,stribution is given as: μ=(a+b)/20.385=(0+b)/2b=0.77 The varianfor a U(a,stribution is given as: σ2=(b−a)2/12\sigma^2=(b-a)^2/12σ2=(b−a)2/120.086=b2/120.086=b^2/120.086=b2/12b=1.016b=1.016b=1.016老师您看我写的不明白的地方总体方差不应该是(样本方差的均值*15)/14吗?

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