Re: [機統] 求multinomial 的marginal

[carteregg (EGG)]

※ 引述《Hshs (免錢沒人愛@@)》之銘言：
: Let X1 and X2 have the following joint probability mass function:
: P[X1=a,X2=b]=[n!/(a!b!(n-a-b)!)]*p1^a* p2^b*(1-p1-p2)^(n-a-b)
: X1,X2>0 X1+X2<=n
: Find the marginal distribution of X1
: 我想應該要把他組合成像binomail
:              n-a
: n!/((n-a)!a!)Σ (n-a)!/b!(n-a-b)!*p1^a* p2^b*(1-p1-p2)^(n-a-b)
:              b=0
: 在這就卡住了@@ 有甚麼技巧嗎?  謝謝


                   n-a
= n!/((n-a)!a!)p1^aΣ (n-a)!/b!(n-a-b)!* p2^b*(1-p1-p2)^(n-a-b)
                   b=0


=n!/((n-a)!a!)p1^a(1-p1)^(n-a)


=>X1~BIN(n,p1)

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