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蟯螻旧 覯 伎觜襦 一讌螻,
旧 蠍磯.

Contents

1
2 螻 覲瑚概螳
3 覲牛(compound event)
4 襯 螳
5 襯 螻給Μ 覯豺
6 襴曙螻 襯
7 覿
8 覯伎 襴

[http]EXCEL 糾, 螳蠍, 一, 覦襯 襴.

1 #

  • 覿れ燕 蟆一 蠍 伎 覈讌 轟煙 豸″ 襯 覿蟇磯 企 蟆郁骸螳 覦 磯ゴ 覿螻 企ゼ 豕 襯 .
  • 襯螻 豢襴糾螻朱 蟯螻,
    • 襯 覈讌朱覿 覲語 (一)
    • 豢襴糾 覲語朱覿 覈讌 豢襦(蠏)

2 螻 覲瑚概螳 #

  • ろ(experiment)企 譟郁唄 蟯豸′企 豸′ 覦 螻殊
  • 蠍磯蓋蟆郁骸(basic outcom)企 覃 結伎 覦 蟆郁骸
  • 覲瑚概螳(sample sapce) ろ れ襦 蟯谿壱 螳ロ 覈 蠍磯蓋蟆郁骸(殊) 讌
  • (event) 襯ろ れ襦 視 伎 蠍磯蓋蟆郁骸れ 讌

3 覲牛(compound event) #

  • (union of event) 覲瑚概螳 企 覈 螳企 企 覈 殊れ 讌
  • 蟲(intersection of event) 覲瑚概螳 企 覈 螻牛旧朱 讌
  • (complement of A)企 覲瑚概螳 覈 譴 轟 讌 殊 讌

4 襯 螳 #

螳蟯 襯
  • 螻 覦覯(企 覦覯)
    • 企れ 100覈企. 譴 40覈企. 1覈 豢豢 蟆曙 襯?
    • 60/100 = 0.6
  • 蟆渚 覦覯( 螳 伎)
    • 螻手碓 900 覿 螳企 覿 100. 螻糾螳 螳 覿 襯? (蠏)
    • 100/900 = 0.11
  • 蟆渚 覦覯 襯 蟆 蟆渚レ .

5 襯 螻給Μ 覯豺 #

螻給Μ
  • 螻給Μ1: 0 <= P(A) <= 1
  • 螻給Μ2: P(S) = 1
  • 螻給Μ3: P(A or B) = P(A) + P(B)

覯豺
  • 覯豺(螻給Μ3朱覿)
    • P(A or B) = P(A) + P(Ac) = 1
    • P(Ac) = 1 - P(A)
  • ъ 覯豺
    • P(AB) = P(A) + P(B) - P(AB)
    • P(AB)襯 觜朱 伎 螻牛給覿 譴覲 螻一 狩蠍
    • 碁旭企朱 譴覲給 覿覿 る 蟆. 蠏碁覩襦 P(AB) = 0 .
  • 譟郁唄襯(蟆壱襯 谿瑚)
    • 覦 蟯螻螳 伎 襯 るジ 覦 レ 覦 蟆曙
    • 譬 蟆曙磯 伎螻 螳 覲螻 譯手, 觜覲旧豢豢(sampling without replacement)
      • P(A|B) = P(AB) / P(B)
      • 企 B螳 企 覦る 譟郁唄 A螳 覦 襯
    • 觜譬 蟆曙磯 貊ろ 讌 伎 螳 襷 蟆, 覲旧豢豢(sampling with replacement)
      • P(B|A) = P(B) P(A|B) = P(A)
      • P(A) P(B) 覓伎^蟇 襯(unconditional probability), 譯朱 襯(marginal probibility) 襯(simple probiblility) 手 .
  • 螻煙覯豺( 蟆壱襯 = P(AB))
    • 譟郁唄襯 P(A|B) = P(AB) / P(B)
    • 覲 P(B)襯 螻燕覃 P(B)P(A|B) = P(B)P(AB) / P(B)
    • P(AB) = P(B)P(A|B)
    • 襷, A 觜螳 覦蟇磯 一朱 覦 蟆壱襯 P(AB) = P(A)P(B)
  • 蟆磯朱..
    • P(A|B) = P(A) P(B|A) = P(B)
    • P(AB) = P(A)P(B)
    • 譟郁唄 焔渚讌 朱 譬朱 覲伎 .

6 襴曙螻 襯 #

企 豢蟲 襯 4/9, 襯 3/9, 覓 襯 2/9企. 5 2覓 3 襯?

豌 蟆曙一 10! / (5!2!3!)

蟆曙一 (4/9)5(2/9)2(3/9)3

蠏碁覩襦 襯..
(10! / (5!2!3!)) * (4/9)5(2/9)2(3/9)3

7 覿 #

覦煙
35540
152540
503080

譯朱襯
  • 譯朱襯 覿(contingency table) 譯朱(margin) 蠍 覓語 覿讌 企
  • P(覦煙) = 50/80 = 0.625
  • P() = 30/80 = 0.375
  • P() = 40/80 = 0.5
  • P() = 40/80 = 0.5

蟆壱襯
  • P(覦煙呉) = 35/80 * 40/80 = 0.4375
  • P(覦煙呉) = 15/80 * 40/80 = 0.1875
  • P(呉) = 05/80 * 40/80 = 0.0625
  • P(呉) = 25/80 * 40/80 = 0.3125

蟆壱襯覿
覦煙
0.43750.06250.5
0.18750.31250.5
0.6250.3751.0

譬 蟆曙一 譟郁唄 襯
  • 語 譬瑚?
  • P() = 40/80 = 0.5
  • P(|) = P(呉) / P() = 0.0625 / 0.5 = 0.125 ( 語 蟆曙) --> 譬企.
  • 襷 P() = P(|) 朱 襴曙企.

8 覯伎 襴 #


  • 襯(prior probablility)
  • 襯(posterior probability)
  • 豢螳 覲 覲伎 螳 襯 蟆曙 襯襦 襷 覯伎 襴(bayes' theorem)螳 伎
  • 覯伎 襴 襯螻 譟郁唄襯
  • P(L1|D) = P(L1)P(D|L1) / P(L1)P(D|L1) + P(L2)P(D|L2)
  • P(L2|D) = P(L2)P(D|L2) / P(L1)P(D|L1) + P(L2)P(D|L2)


讌 磯殊語 磯 るゴ. れ螻 螳 譯殊伎り .

覿襯
L10.990.010.55
L20.950.050.45

  • 覿 覦蟆 蟆曙 螳 殊 L1, L2 襯?
  • 襯 L1 = 0.55, L2 = 0.45
  • P(L1|覿) = 0.55(0.01) / (0.55 * 0.01 + 0.45 * 0.05) = 0.1964
  • P(L2|覿) = 0.45(0.55) / (0.55 * 0.01 + 0.45 * 0.05) = 0.8036
蠍 蠍郁鍵..
企: : るジ讓曙 襦螻豺 企Ν 譯殊語. 襦螻豺
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