更新1:
∫R[e^(-(R)/θ)][1-e^(-(R)/θ)]^(n-2) dR = 1 Reason? Computing ∫ (n-1)(R^2/θ)[e^(-(R)/θ)][1-e^(-(R)/θ)]^(n-2) dR is more difficult.
更新2:
The revised answer is problematic, can the mean be independent of n?
Order Statistics (2)
2008-03-28 9:21 pm
What is the sampling distribution of sample range of size n from an exponential population? Please find its mean and variance.
回答 (3)
2008-04-11 7:38 pm
✔ 最佳答案
In statistics, the kth order statistic of a statistical sample is equal to its kth-smallest value. Together with rank statistics, order statistics are among the most fundamental tools in non-parametric statistics and inference.Important special cases of the order statistics are the minimum and maximum value of a sample, and (with some qualifications discussed below) the sample median and other sample quantiles.
When using probability theory to analyze order statistics of random samples from a continuous distribution, the cumulative distribution function is used to reduce the analysis to the case of order statistics of the uniform distribution.
但係妳呢條太難, 我唔識答....
參考: 花公公
2008-04-02 6:05 pm
If the mean is independent of n, since when n = 1, the range is actually deterministic to be 0, the mean of the range has to be zero.
2008-04-02 10:05:47 補充：
But range is defined as the absolute difference between the largest and the smallest sample, it has 0 probability to be smaller than 0, the mean is highly unlikely to be 0.
2008-04-02 10:05:47 補充：
But range is defined as the absolute difference between the largest and the smallest sample, it has 0 probability to be smaller than 0, the mean is highly unlikely to be 0.
2008-03-29 5:42 am
計到了﹐順便計到53﹐可惜要遲些才post到
2008-04-02 16:49:20 補充：
我估要找叮噹出馬
2008-04-02 16:49:20 補充：
我估要找叮噹出馬
收錄日期: 2021-04-23 13:01:46
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20080328000051KK01316