Re: expected value for sampling without replacement


J Jensen wrote:
> Ok, in sampling without replacement, I sequentially draw
> X_1, X_2, ... X_n
>
> Obviously E(X_1) = μ but why should E(X_3) = μ ?
>
> E(X_3) = Σ c_i P(X_3 = c_i)
>
> and the probabilities are all different since items have been taken
out
> and not replaced...
>
> --Jeff


Imagine you draw the n values on cards, and lay the cards face down on
a table before looking at them. X_1 is the value of the card in the
first position, X_2 is the value of the card in the second position,
and so on. If you now switched X_3 with X_1, the resulting draw is just
as much a random draw without replacement as the original. So X_3 has
the same distribution as X_1.

Mike

.

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