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Example 5.6<br />
Consider a sequence of independent random variables X n that are<br />
uniformly distributed in the interval [0, 1], and let<br />
Y n min(X 1 , . . . , X n ).<br />
Does Y 1 , Y 2 , . . . converge to zero in probability<br />
說 明<br />
P(|Y n − 0| ≥ ɛ) = (1 − ɛ) n<br />
n→∞<br />
−−−→ 0.<br />
Chia-Ping Chen ( 中 山 資 工 ) Limit Theorems 機 率 學 講 義 17 / 28
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