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ralph318 · 2021年09月03日

这一题c小题算出b=0.77,但是题目里明明就有不在【0,0.77】范围内的数字,这是怎么回事呢?

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

如果这个数列是【0,b】的话,应该所有数字都是大于等于0,小于等于0.77才对啊?

1 个答案

品职答疑小助手雍 · 2021年09月03日

嗨,从没放弃的小努力你好:


emmm是不能出现超过均匀分布上下限的数字的,主要是因为c这里是按均值估的分布范围(这种估法本身就是不准的),所以就忽略了0.96那个数字了,确实不严谨。

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

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