http://i.imgur.com/QUObfzg.png
想請問紅色字部份，為什麼會用到sumation加總呢？
像是求x,y的邊際分配，都不會用到加總，
不太了解為什麼這邊會用到？
統計題目：求三項分配，當Z=X+Y的機率分配?
2017-03-01 10:25 pm
回答 (1)
2017-03-02 10:03 pm
Sol
f(z)=P(Z=z)
=P(X+Y=z)
=P(X=0)*P(X+Y=z｜X=0)+P(X=1)*P(X+Y=z｜X=1)+P(X=2)*P(X+Y=ｚ｜X=2)
+…+ P(X=z)*P(X+Y=ｚ｜X=z)
=Σ(x=0 to z)_ P(X=x)*P(X+Y=z｜X=x)
=Σ(x=0 to z)_ P(X=x)*P(x+Y=z｜X=x)
=Σ(x=0 to z)_ P(X=x)*P(Y=z－x｜X=x)
=Σ(x=0 to z)_ P(X=x)*[P(Ｘ=x，Y=z－x)/P(X=x)]
=Σ(x=0 to z)_P(Ｘ=x，Y=z－x)
f(z)=P(Z=z)
=P(X+Y=z)
=P(X=0)*P(X+Y=z｜X=0)+P(X=1)*P(X+Y=z｜X=1)+P(X=2)*P(X+Y=ｚ｜X=2)
+…+ P(X=z)*P(X+Y=ｚ｜X=z)
=Σ(x=0 to z)_ P(X=x)*P(X+Y=z｜X=x)
=Σ(x=0 to z)_ P(X=x)*P(x+Y=z｜X=x)
=Σ(x=0 to z)_ P(X=x)*P(Y=z－x｜X=x)
=Σ(x=0 to z)_ P(X=x)*[P(Ｘ=x，Y=z－x)/P(X=x)]
=Σ(x=0 to z)_P(Ｘ=x，Y=z－x)
收錄日期: 2021-04-30 22:09:50
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20170301142525AAmIjy3