random variable X,

random variable Y1,Y2,Y3...Yn are  independent identically distributed

we have known P(X=1|Y=y)=f(y);

consider

P(X=1|Y1=y1)=f(y1), P(X=1|Y2=y2)=f(y2),......P(X=1|Yn=yn)=f(yn),

will f(y1),f(y2),..,f(yn) be the same?

will f(y2)* f(y2)* f(yn)=f(y)n?

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