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1 螳 #
- 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)
- 襯 覈讌朱覿 覲語 (一)
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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
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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
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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
- 企れ 100覈企. 譴 40覈企. 1覈 豢豢 蟆曙 襯?
- 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
- 螻手碓 900 覿 螳企 覿 100. 螻糾螳 螳 覿 襯? (蠏)
- 蟆渚 覦覯 襯 蟆 蟆渚レ .
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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(螻給Μ3朱覿)
- P(A or B) = P(A) + P(Ac) = 1
- P(Ac) = 1 - P(A)
- P(A or B) = P(A) + P(Ac) = 1
- 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 .
- P(AB) = P(A) + P(B) - P(AB)
- 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
- P(A|B) = P(AB) / P(B)
- 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 .
- P(B|A) = P(B) P(A|B) = P(A)
- 覦 蟯螻螳 伎 襯 るジ 覦 レ 覦 蟆曙
- 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)
- 譟郁唄襯 P(A|B) = P(AB) / 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 .
- P(A|B) = P(A) P(B|A) = P(B)
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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!)
| 覓 | 覓 |
蠏碁覩襦 襯..
(10! / (5!2!3!)) * (4/9)5(2/9)2(3/9)3
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7 覿 #
| 覦煙 | 螻 | ||
| 35 | 5 | 40 | |
| 15 | 25 | 40 | |
| 螻 | 50 | 30 | 80 |
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
- 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
| 覦煙 | 螻 | ||
| 0.4375 | 0.0625 | 0.5 | |
| 0.1875 | 0.3125 | 0.5 | |
| 螻 | 0.625 | 0.375 | 1.0 |
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.
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8 覯伎 襴 #
螳
讌 磯殊語 磯 るゴ. れ螻 螳 譯殊伎り .
- 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 .
| 襯 | 覿襯 | 一 | |
| L1 | 0.99 | 0.01 | 0.55 |
| L2 | 0.95 | 0.05 | 0.45 |
- 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
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