statistic 上有 d 概念唔明

1 mean of all possible sample mean = population mean

除非那個sample mean是unbiased estimator﹐否則上式不一定成立。

mean of all possible sample mean 和 normal distribution 沒有關係。原則上是當您抽的sample 數目夠大 (>30)。則您描出來的這些sample 會服從 normal distribution。所以您可以用這些sample的平均值作為population mean﹐然後再根據normal distribution table 找出 population 內某個範圍數值的機率。

2 95% confidence interval 表示當重複做100次試驗﹐100個confidence interval 中會有95個包含了population mean 。不過我們沒有可能知道那一個(些) confidence interval 是真的包含了population mean 。所以confidence interval 不能決定population mean 的真實數值之餘也是不能決定population mean 的range的。

3 sorry。

2010-04-08 18:36:06 補充：
你找了A股派息記錄的30 個sample﹐然後可以計到sample mean。這個可以作為A股 rate of return 的一個estimation。但是股票不是有形產品﹐例如燈泡。所以我想沒有所謂population mean 的。

這裏可以幫到你
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1: It is Central Limit Theorm. You could use normal distribution to approximate any distribution if the sample size is large

2: Yes. You could never find out the exact answer of population mean, unless you get the poplulation distribution. Sample is just a unbiased and consistent estimation of population (just an estimation). It could be proved that sample mean would trend to converge to the population mean if the sample size (n) is large. However, it is not certain (Pr < 1.0). Hence, we need to have a confidence interval to measure how confidence we have on the estimation.

3: You could apply Binomial Thorey on the estimation of stock price

possible increase in stock price = u%
possible decrease in stock price = d%
stock price at time t = St
S0 is known


2010-04-12 18:28:14 補充：
For the estimation of dividends, it is better to apply time series analysis to model the trend. There may be seasonal effect on the dividend (e.g. 中期息,末期息,特別息,etc.).

Since the dividend may not be random in nature, it is not appropriate to apply Normal Distribution.

2010-04-17 14:56:36 補充：
for binominal option pricing or stock pricing, please see http://faculty.darden.virginia.edu/conroyb/derivatives/Binomial%20Option%20Pricing%20_f-0943_.pdf