21032015Group3_Multinomial distribution.pptx

Statistical Learning Methods

Phn phi a thcCopyright, 1996 Dale Carnegie & Associates, Inc.Multinomial Distribution20152Gii thiuPhn phi a thc l mt phn phi xc sut ri rc, l mt dng tng qut ca phn phi nh thc

3Gii thiuNh chng ta bit, phn phi nh thc m t mt qu trnh Bernoulli cho mt bin chung X, vi mt lot cc gi tr cho cc th nghim duy nht trn X m bao gm trong 0 v 1, vi 1 l thnh cng v tht bi l 0.Cc a thc, thay vo , m s ln m mt th nghim cho mt gi tr nht nh. V d, s ln m tung mt con xc xc cho mi mt mt (1,2,3,4,5,6).4Cng thc ca phn phi a thcGing nh BD, MDF c mt cng thc tnh ton gi tr ca n, nh sau:

4What is P(hi|d)?5Cng thc ca phn phi a thcGing nh BD, chng ti c mt khng gian mu l s n. Mi ni, (i: 1..s) xc nh gi tr ca mi kt qu cho xi. i vi v d con xc xc, mi ni tng trng cho s ln m n xut hin mt i.Sau , pi tng trng cho xc sut ca mi ln th nghim a ra kt qu xi.Cui cng, cc h s tng quan a thc m tt c s kt hp c th c ca kt qu n1 cho kt qu x1, n2 cho kt qu x2, v.v6Thuc tnh ca phn phi a thcCc thuc tnh chnh ca phn phi a thc l mi lin h v gi tr ca pi v ni :n = ni, tng ca tt c cc kt hp c th c cho chng ta khng gian ca mu;. pi = 1, tng cc xc sut c th xy ra l 1 (nh i vi BD).7K vng v phng saiGi tr k vng cho MD l nh sau:E[M] = n*(p1, , ps)V phng sai:Var[M] = n*pi*(1 - pi)iu ny l ng i vi thuc tnh sau y: Nu S = (S1, ..., Ss) l mt vector may ri sau phn phi a thc ca cc thng s ((p1, ..., ps), n), mi Si c th c coi l mt bin nh thc "

8K vng v phng saii vi gi tr k vng ta c:E[S]=(E[S1],,E[Ss])=nE[X]=n*(p1, , ps) =(np1, ,nps) V phng sai:Si,i =n*Var[Si] = n*pi*(1 - pi)bi v chng ta bit rng vic phn phi nh thc c k vng n*p v phng sai n*p*(1-p).9V d 1: tung xc xcLy v d con xc xc gii thch t u, chng ta c th ni rng s lng cc kt qu c m t bi mi mt sau phn phi a thc vi cc thng s ((1/6, 1/6, 1/6, 1/6, 1/6, 1 / 6), n).Nu chng ta ni rng mt 6 xut hin 1 ln, 5 xut hin 2 ln, 4 xut hin 4 ln, 3 xut hin 0 ln, 2 xut hin 2 ln v 1 xut hin 3 ln, ta c n = 12.10V d 1: tung xc xcV vy, chng ta c th tnh ton xc sut ca th nghim ny l:

V vy, trong trng hp c bit ny, chng ta c mt xc sut rt nh.

11Tng ktKhi chng ta c mt phn phi m c v nh l mt phn phi nh thc, nhng chng ta c kt qu khc nhau cho tng i tng tham gia th nghim, chng ta c th s dng phn phi a thc. 12V d: Lut chi:2 mu cam, 3 mu xanh, 4 mu vng, 1 mu Ly 1 tri banh ra v tr tr vLp li 4 lnNu ly c 3 mu vng v 1 mu cam l WIN!13Xc sut:

5%

14V d: Lut chi:Rt 1 l bi t 4 b bi khc nhauNu rt c Jack hoc hn Jack (J,Q,K,A) cho tt c 4 l bi l WIN!15Xc sut:

0.9%

16Xin cm n!!!