※ 引述《brooky (未夠班)》之銘言：
: ※ 引述《yabt (痴心絕對)》之銘言：
: : The following is just my guess, it may not be correct :)
: Thank you very much.
: Your explanation is quite clear and useful.
: : Note that some functions of the samples T(X1, X2, ..., Xn) would follow the
: : sample distribution of T(X) no matter with or without replacement, where
: : X1~Xn are random variables of the samples, and X is the real random variable
: : of the underlying model. The average function T = sum(Xi)/n is a good example.
: : There are also some functions such that their distributions are not the same,
: : for instance, T(X) = X2, the transform that we only keep the result of the
: : second sample.
: May I ask one more question?
: I do not understand the description,
: "soe functions of the the samples T(X1, X2, ..., Xn) would follow
: the sample distribution of T(X)".
: Does that mean T(X1, X2, ..., Xn) will reflect the real distribution of T(X)?
: Is there any definition or rule to decide whether one distribution is
: following another one?
: Thank you for your responses and all your time.
: : What's more, consider the case that the size of the data is large. The former
: : sample from, say 1000:1000, will not affect the probability distribution of
: : the later sample that much, say 1000:999. That's why sampling without
: : replacement is OK only if we have a large data set.
Sorry I have to revise the description I gave here. What I mean is,
if the RV X1~Xn stand for the result sampling w/o replacement,
and the RV Y1~Yn stand for the result sampling w/ replacement,
then some functions T would make the dirstribution of T(X1, X2, ..., Xn)
identical to the distribution of T(Y1, Y2, ..., Yn).
The expression about T(X) my misunderstanding.
In addition, the example T(X1, ...Xn) = X2 do gives the identical distribution
with T(Y1, ...Yn) = Y2. The marginal probability P(X2 = head) do equals
P(Y2 = head), but the conditional probability P(X2 = head | X1 = head) does
not equal P(Y2 = head | Y1 = head). X1, X2, ..., Xn still have idential
distribution as Ys', but they are not independent, while Ys' are.