开发者:上海品职教育科技有限公司隐私政策详情

应用版本:4.2.11(IOS)｜3.2.5(安卓)APP下载

学习体验
App下载
手机上的品职教育

随时随地学习课程，支持音视频下载！
- 扫码下载品职教育APP
进入课程
登录 | 注册

比如世界 · 2020年04月06日

问一道题：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)

$\mu = n^{-1}\sum_{i=1}^{n}X_i =0.39$

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

b.The sample mean is already unbiased.

For the variance:

$s^2=n\sigma^2/(n-1) =15*0.080/14=0.086$

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:

$\sigma^2=(b-a)^2/12$

$0.086=b^2/12$

$b=1.016$

问题：unbiased estimators of the variance，这个指标衡量的是什么，公式是怎么得到的？

添加评论

0
0

1 个答案

袁园_品职助教 · 2020年04月07日

同学你好！

在 “The Moments” 这一节视频里讲过，公式如图：

添加评论

0
0

1
回答
0
关注
369
浏览

我要回答关注问题

相关问题

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=1nXi=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？

2024-05-13 15:24 1 · 回答

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 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=1nXi=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 总体是Uniform的话，样本一定是uniform吗？如果是的话，可以用（0.95-0）/2来计算样本均值吗

2024-04-23 10:51 1 · 回答

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=1nXi=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样本均值应等于A加B然后除以2；无偏均值就是该均值。样本方差等于B减去A 平方然后除以12。解题公式不知道什么意思。最后两问不知道在说什么。均匀分布到底应该怎么计算？谢谢。尤其是最后两个问题在说什么。感觉均匀分布前提和适用场景特别不清楚。烦请详细说明，谢谢

2023-03-26 06:04 1 · 回答

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=1nXi=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=1.016a求的是sample variance，为什么分母不是除以n-1 呢？

2023-01-25 17:16 1 · 回答

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=1nXi=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第三问和第四问求具体解析及教程是哪一页有讲到啊？

2022-09-25 14:36 1 · 回答