표본분포

Chap 6. 표본분포

6.2 Random 추출법

Def. Let X_1, X_2, ..., X_n be a collection of n random variables. These random variables are said to constitute a random sample of size n if
a) the X_i are independent random variables, and
b) every X_i has the same probability distribution.

6.3 표본분포

Def. Suppose p(x) depends on a quality that can be assigned any one of a number of possible values, with each different value determining a different probability distributions. Such a quality is called a parameter.
Def. A Statistic is any function of the random variables constituting one or more samples, provided that the function does not depend on any unknown parameter values.
Def. Often we are able to determine the probability distribution of a particular statistic if we know the probability distribution from which the sample was drawn. The probability distribution of a statistic is called a sampling distribution.
Def. The random variables \bar X = 1/n \sum_i=0^n X_i is called a sample mean of the sample X_1, X_2, ..., X_n.
Cor. When E(X_i)=\mu for i=1,...,n, E(\bar X)=\mu.
Cor. When Var(X_i)=\sigma for i=1,...,n, Var(\bar X)=\sigma/n.

6.4 표본분포의 모형과 중심극한정리

Thm. The Central Limit Theorem (C.L.T.)
Let X_1, X_2, ..., X_n be a random sample from a distribution with mean and variance . Then if n is sufficiently large, \bar X has approximately a normal distribution with \mu_{\bar X}=\mu and \sigma^2_{\bar X}=\sigma^2/n.
Note. If n>30, the C.L.T. can be used

Quiz 4. Email: lbg@kowon.dongseo.ac.kr