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本章內容馬可夫不等式 Markov inequality 契比雪夫不等式 Chebyshev inequality 隨機變數序列 sequence of random variables 弱大數法則 weak law of large numbers 強大數法則 strong law of large numbers 中央極限定理 central limit theorem Chia-Ping Chen ( 中山資工 ) Limit Theorems 機率學講義 2 / 28
馬可夫不等式 X 為非負的隨機變數 ,a > 0, 則以下不等式成立 , 稱為馬可夫不等式 P(X ≥ a) ≤ E[X ] a . 證明令 Y a (X ) (X < a) 0 : a. 則 Y a ≤ X ⇒ E[Y a ] ≤ E[X ] ⇒ a P(X ≥ a) ≤ E[X ] ⇒ P(X ≥ a) ≤ E[X ] a . Chia-Ping Chen ( 中山資工 ) Limit Theorems 機率學講義 3 / 28
Page 1: 極限定理陳嘉平國立
Page 5 and 6: Example 5.1 & 5.2 Let X be uniforml
Page 7 and 8: 隨機變數序列由隨機
Page 9 and 10: 樣本和樣本和 S n 的期
Page 11 and 12: 規範化樣本平均規範
Page 13 and 14: 估計的確度與信度作
Page 15 and 16: 隨機變數序列的收斂
Page 17 and 18: Example 5.6 Consider a sequence of
Page 19 and 20: 幾乎確定性收斂隨機
Page 21 and 22: 大數法則假設隨機變
Page 23 and 24: 中央極限定理隨機變
Page 25 and 26: Example 5.9 We load on a plane 100
Page 27 and 28: Example 5.11 We poll n voters and r

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