多变量条件概率公式三个变量时P(W|S)=P(W|R,S)P(R|S)+P(W|~R,S)P(~R|S)公式的由来.以及四个变量时.p(w|c)=p(w|R,s,c)p(R,s|c)+P(W|~R,S,C)P(~R,S|C)+P(W|R,S,C)P(R,S|C)+P(W|~R,S,C)P(~R,S|C)这个公式的由来.
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![多变量条件概率公式三个变量时P(W|S)=P(W|R,S)P(R|S)+P(W|~R,S)P(~R|S)公式的由来.以及四个变量时.p(w|c)=p(w|R,s,c)p(R,s|c)+P(W|~R,S,C)P(~R,S|C)+P(W|R,S,C)P(R,S|C)+P(W|~R,S,C)P(~R,S|C)这个公式的由来.](/uploads/image/z/2532464-8-4.jpg?t=%E5%A4%9A%E5%8F%98%E9%87%8F%E6%9D%A1%E4%BB%B6%E6%A6%82%E7%8E%87%E5%85%AC%E5%BC%8F%E4%B8%89%E4%B8%AA%E5%8F%98%E9%87%8F%E6%97%B6P%EF%BC%88W%7CS%EF%BC%89%3DP%EF%BC%88W%7CR%2CS%EF%BC%89P%EF%BC%88R%7CS%EF%BC%89%2BP%EF%BC%88W%7C%7ER%2CS%EF%BC%89P%EF%BC%88%7ER%7CS%EF%BC%89%E5%85%AC%E5%BC%8F%E7%9A%84%E7%94%B1%E6%9D%A5.%E4%BB%A5%E5%8F%8A%E5%9B%9B%E4%B8%AA%E5%8F%98%E9%87%8F%E6%97%B6.p%28w%7Cc%29%3Dp%28w%7CR%2Cs%2Cc%29p%28R%2Cs%7Cc%29%2BP%28W%7C%7ER%2CS%2CC%29P%28%7ER%2CS%7CC%29%2BP%28W%7CR%2CS%2CC%29P%28R%2CS%7CC%29%2BP%28W%7C%7ER%2CS%2CC%29P%28%7ER%2CS%7CC%29%E8%BF%99%E4%B8%AA%E5%85%AC%E5%BC%8F%E7%9A%84%E7%94%B1%E6%9D%A5.)
多变量条件概率公式三个变量时P(W|S)=P(W|R,S)P(R|S)+P(W|~R,S)P(~R|S)公式的由来.以及四个变量时.p(w|c)=p(w|R,s,c)p(R,s|c)+P(W|~R,S,C)P(~R,S|C)+P(W|R,S,C)P(R,S|C)+P(W|~R,S,C)P(~R,S|C)这个公式的由来.
多变量条件概率公式
三个变量时P(W|S)=P(W|R,S)P(R|S)+P(W|~R,S)P(~R|S)公式的由来.
以及四个变量时.p(w|c)=p(w|R,s,c)p(R,s|c)+P(W|~R,S,C)P(~R,S|C)+P(W|R,S,C)P(R,S|C)+P(W|~R,S,C)P(~R,S|C)这个公式的由来.
多变量条件概率公式三个变量时P(W|S)=P(W|R,S)P(R|S)+P(W|~R,S)P(~R|S)公式的由来.以及四个变量时.p(w|c)=p(w|R,s,c)p(R,s|c)+P(W|~R,S,C)P(~R,S|C)+P(W|R,S,C)P(R,S|C)+P(W|~R,S,C)P(~R,S|C)这个公式的由来.
P(W|S)=P(W,S)/P(S)
P(W|R,S)P(R|S)=[P(W,R,S)/P(R,S)][P(R,S)/P(S)]=P(W,R,S)/P(S)
P(W|~R,S)P(~R|S)=[P(W,~R,S)/P(~R,S)][P(~R,S)/P(S)]=P(W,~R,S)/P(S)
同时:P(W,R,S)/P(S)+P(W,~R,S)/P(S)=[P(W,R,S)+P(W,~R,S)]/P(S)=P(W,S)/P(S)
所以P(W|S)=P(W|R,S)P(R|S)+P(W|~R,S)P(~R|S)
四个变量时用相同方法证明,你自己证明吧.