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Contents

1 媛쒖슂
2 궗긽怨 몴蹂멸났媛
3 蹂듯빀궗긽(compound event)
4 솗瑜좎쓽 媛쒕뀗
5 솗瑜좎쓽 怨듬━ 踰뺤튃
6 룆由쎌떆뻾怨 솗瑜
7 遺꾪븷몴
8 踰좎씠利 젙由

[http]EXCEL 솢슜 쁽 넻怨꾪븰, 媛뺢툑떇, 젙슦꽍, 諛뺤쁺궗瑜 젙由ы뻽떎.

1 媛쒖슂 #

  • 遺덊솗떎꽦븯뿉꽌 쓽궗寃곗젙쓣 븯湲 쐞빐꽌뒗 紐⑥쭛떒쓽 듅꽦쓣 삁痢≫븯뒗뜲 솗瑜좎쓣 遺뿬븯嫄곕굹 뼱뼡 寃곌낵媛 諛쒖깮븯뒗 뜲 뵲瑜대뒗 쐞뿕쓣 遺꾩꽍븯怨 씠瑜 理쒖냼솕븯뒗뜲 솗瑜좎쓣 쟻슜븳떎.
  • 솗瑜좉낵 異붾━넻怨꾪븰怨쇰뒗 뿭쓽 愿怨,
    • 솗瑜좎 紐⑥쭛떒쑝濡쒕꽣 몴蹂몄쓣 뙋떒(뿰뿭)
    • 異붾━넻怨꾪븰 몴蹂몄쑝濡쒕꽣 紐⑥쭛떒뿉 븳 異붾줎(洹궔)

2 궗긽怨 몴蹂멸났媛 #

  • 떎뿕(experiment)씠 쑀궗븳 議곌굔븯뿉꽌 愿痢≪씠굹 痢≪젙쓣 쑀諛쒗븯뒗 怨쇱젙
  • 湲곕낯寃곌낵(basic outcom)씠 룞쟾쓽 븵硫 삉뒗 뮮硫댁쿂읆 룞떆뿉 諛쒖깮븷 닔 뾾뒗 寃곌낵
  • 몴蹂멸났媛(sample sapce) 떎뿕쓽 떎떆濡 愿李고븷 닔 엳뒗 媛뒫븳 紐⑤뱺 湲곕낯寃곌낵(떒씪궗긽)쓽 吏묓빀
  • 궗긽(event) 솗瑜좎떎뿕쓽 떎떆濡 뼸뒗 븯굹 씠긽쓽 湲곕낯寃곌낵뱾쓽 吏묓빀

3 蹂듯빀궗긽(compound event) #

  • 빀궗긽(union of event) 몴蹂멸났媛꾩쓣 씠猷⑤뒗 紐⑤뱺 궗긽 媛슫뜲 쟻뼱룄 븯굹쓽 궗긽뿉 냽븯뒗 紐⑤뱺 떒씪궗긽뱾쓽 吏묓빀
  • 援먯궗긽(intersection of event) 몴蹂멸났媛꾩쓣 씠猷⑤뒗 紐⑤뱺 궗긽뿉 怨듯넻쟻쑝濡 냽븯뒗 떒씪 궗긽쓽 吏묓빀
  • 뿬궗긽(complement of A)씠 몴蹂멸났媛꾩뿉 냽븯뒗 紐⑤뱺 떒씪 궗긽 以묒뿉꽌 듅젙 궗긽뿉 냽븯吏 븡뒗 떒씪궗긽쓽 吏묓빀

4 솗瑜좎쓽 媛쒕뀗 #

媛앷쟻 솗瑜
  • 怨좎쟾쟻 諛⑸쾿(씠濡좎쟻 諛⑸쾿)
    • 븳 겢옒뒪뿉 븰깮 100紐낆씠떎. 씠 以묒뿉꽌 궓옄뒗 40紐낆씠떎. 1紐 異붿텧븷 寃쎌슦 뿬옄씤 솗瑜좎?
    • 60/100 = 0.6
  • 寃쏀뿕쟻 諛⑸쾿(긽룄닔 媛쒕뀗 씠슜)
    • 怨쇨굅뿉 궔뭹븳 900긽옄쓽 遺뭹 媛슫뜲 遺덈웾뭹 100긽옄떎. 씠 怨듦툒옄媛 궔뭹븷 긽옄媛 遺덈웾뭹씪 솗瑜좎? (洹궔)
    • 100/900 = 0.11
  • 寃쏀뿖쟻씤 諛⑸쾿쓽 솗瑜좎씠 넂寃 굹뒗 寃쏀뼢씠 엳떎.

5 솗瑜좎쓽 怨듬━ 踰뺤튃 #

怨듬━
  • 怨듬━1: 0 <= P(A) <= 1
  • 怨듬━2: P(S) = 1
  • 怨듬━3: P(A or B) = P(A) + P(B)

踰뺤튃
  • 뿬궗긽쓽 踰뺤튃(怨듬━3쑝濡쒕꽣)
    • P(A or B) = P(A) + P(Ac) = 1
    • P(Ac) = 1 - P(A)
  • 뜤뀍 踰뺤튃
    • P(A닼B) = P(A) + P(B) - P(A닶B)
    • P(A닶B)瑜 鍮쇰뒗 씠쑀뒗 怨듯넻遺遺꾩뿉 븳 以묐났 怨꾩궛쓣 뵾븯湲 쐞븿
    • 몢 궗긽씠 긽샇諛고쟻씠씪硫 以묐났릺뒗 遺遺꾩씠 뾾떎뒗 寃. 洹몃윭誘濡 P(A닶B) = 0 씠 맂떎.
  • 議곌굔솗瑜(寃고빀솗瑜좏몴 李멸퀬)
    • 몢 궗긽씠 諛젒븳 愿怨꾧 엳뼱꽌 븳 궗긽쓽 솗瑜좎씠 떎瑜 궗긽쓽 諛쒖깮뿉 쁺뼢쓣 諛쏅뒗 寃쎌슦
    • 醫낆냽쟻씤 寃쎌슦뒗 씠옄쑉怨 쑀媛 蹂룞怨 二쇨, 鍮꾨났썝異붿텧(sampling without replacement) 벑
      • P(A|B) = P(A닶B) / P(B)
      • 뼱뼡 궗긽 B媛 씠誘 諛쒖깮뻽떎뒗 議곌굔븯뿉꽌 A媛 諛쒖깮븷 솗瑜
    • 鍮꾩쥌냽쟻씤 寃쎌슦뒗 肄붿뒪뵾 吏닔 궡씪 궇뵪媛 留묒 寃, 蹂듭썝異붿텧(sampling with replacement) 벑
      • P(B|A) = P(B) 삉뒗 P(A|B) = P(A)
      • P(A) 삉뒗 P(B)뒗 臾댁“嫄 솗瑜(unconditional probability), 二쇰 솗瑜(marginal probibility) 삉뒗 떒씪 솗瑜(simple probiblility) 씪怨 븳떎.
  • 怨깆뀍踰뺤튃(몢 궗긽쓽 寃고빀솗瑜 = P(A닶B))
    • 議곌굔솗瑜 P(A|B) = P(A닶B) / P(B)
    • 뼇蹂뿉 P(B)瑜 怨깊븯硫 P(B)P(A|B) = P(B)P(A닶B) / P(B)
    • P(A닶B) = P(B)P(A|B)
    • 留뚯빟, A 鍮꾧 룞떆뿉 諛쒖깮븯嫄곕굹 뿰냽쟻쑝濡 諛쒖깮븷 븣 몢 궗긽쓽 寃고빀솗瑜좎 P(A닶B) = P(A)P(B)
  • 寃곕줎쟻쑝濡..
    • P(A|B) = P(A) 삉뒗 P(B|A) = P(B)
    • P(A닶B) = P(A)P(B)
    • 씠 몢 議곌굔씠 꽦由쏀븯吏 븡쑝硫 몢 궗긽 醫낆냽쟻쑝濡 蹂댁븘빞 븳떎.

6 룆由쎌떆뻾怨 솗瑜 #

뼱뒓 異뺢뎄쓽 듅 솗瑜좎 4/9, 뙣 솗瑜좎 3/9, 臾 솗瑜좎 2/9씠떎. 5듅 2臾 3뙣 븷 솗瑜좎?

쟾泥 寃쎌슦쓽 닔뒗 10! / (5!2!3!)

쐞쓽 寃쎌슦쓽 닔 (4/9)5(2/9)2(3/9)3

洹몃윭誘濡 솗瑜좎..
(10! / (5!2!3!)) * (4/9)5(2/9)2(3/9)3

7 遺꾪븷몴 #

諛깆씤쓳씤빀怨
궓옄35540
뿬옄152540
빀怨503080

二쇰솗瑜
  • 二쇰솗瑜좎 遺꾪븷몴(contingency table)쓽 二쇰(margin)뿉 굹굹湲 븣臾몄뿉 遺숈뿬吏 씠由
  • P(諛깆씤) = 50/80 = 0.625
  • P(쓳씤) = 30/80 = 0.375
  • P(궓옄) = 40/80 = 0.5
  • P(뿬옄) = 40/80 = 0.5

寃고빀솗瑜
  • P(諛깆씤닶궓옄) = 35/80 * 40/80 = 0.4375
  • P(諛깆씤닶뿬옄) = 15/80 * 40/80 = 0.1875
  • P(쓳씤닶궓옄) = 05/80 * 40/80 = 0.0625
  • P(쓳씤닶뿬옄) = 25/80 * 40/80 = 0.3125

寃고빀솗瑜좊텇룷
諛깆씤쓳씤빀怨
궓옄0.43750.06250.5
뿬옄0.18750.31250.5
빀怨0.6250.3751.0

醫낆냽쟻씤 寃쎌슦쓽 議곌굔 솗瑜
  • 궓옄 쓳씤 醫낆냽쟻씤媛?
  • P(궓옄) = 40/80 = 0.5
  • P(쓳씤|궓옄) = P(쓳씤닶궓옄) / P(궓옄) = 0.0625 / 0.5 = 0.125 (궓옄씪 븣 쓳씤씪 寃쎌슦) --> 醫낆냽쟻씠떎.
  • 留뚯빟 P(궓옄) = P(쓳씤|궓옄) 씪硫 몢 궗긽 룆由쎌씠떎.

8 踰좎씠利 젙由 #

媛쒕뀗
  • 궗쟾솗瑜(prior probablility)
  • 궗썑솗瑜(posterior probability)
  • 異붽쟻씤 몴蹂 젙蹂댁뿉 엯媛곹븯뿬 궗쟾솗瑜좎쓣 寃쎌떊븯뿬 궗썑솗瑜좊줈 留뚮뱶뒗뜲 踰좎씠利 젙由(bayes' theorem)媛 씠슜맖
  • 踰좎씠利 젙由щ뒗 궗쟾솗瑜좉낵 議곌굔솗瑜좎쓣 쑀룄
  • 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)

삁젣
젣뭹쓽 뭹吏덉 깮궛씪씤뿉 뵲씪 떎瑜대떎. 떎쓬怨 媛숈씠 뼇뭹쑉씠 二쇱뼱議뚮떎怨 븯옄.

뼇뭹瑜遺덈웾뭹瑜깮궛쑉
L10.990.010.55
L20.950.050.45

  • 遺덈웾뭹씠 諛쒓껄맂 寃쎌슦 媛 씪씤 L1, L2쓽 궗썑 솗瑜좎?
  • 궗쟾솗瑜 L1 = 0.55, L2 = 0.45
  • P(L1|遺덈웾뭹) = 0.55(0.01) / (0.55 * 0.01 + 0.45 * 0.05) = 0.1964
  • P(L2|遺덈웾뭹) = 0.45(0.55) / (0.55 * 0.01 + 0.45 * 0.05) = 0.8036
뙎湲 궓湲곌린..
씠由: : 삤瑜몄そ쓽 깉濡쒓퀬移⑥쓣 겢由빐 二쇱꽭슂. 깉濡쒓퀬移
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