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Example 5.11<br />
We poll n voters and record the fraction M n of those polled who are<br />
in favor of a particular candidate. If p is the fraction of the entire<br />
voter population that supports this candidate, then<br />
M n = X 1 + · · · + X n<br />
,<br />
n<br />
where X i ’s are i.i.d. Bernoulli random variables with parameter p.<br />
When n is large,<br />
M n − p = X 1 + · · · + X n − np<br />
n<br />
= X 1 + · · · + X n − np<br />
√ nσ<br />
= Z n<br />
) ≈ Y ).<br />
( √n<br />
( √n<br />
σ √n<br />
σ<br />
σ<br />
Chia-Ping Chen ( 中 山 資 工 ) Limit Theorems 機 率 學 講 義 27 / 28
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