[問題] E(X|X)=X 的證明
E(X|X=x) = sum x * f(X=x|X=x) ................(definition)
= sum x * f(X=x and X=x)/f(X=x)........(definition of f(x|y))
= sum x * f(X=x)/f(X=x)................(f(X=x and X=x) = f(X=x))
= sum x................................(f(X=x)/f(X=x)=1)
?= x...................................(5)
查 google 得到 E(X|X=x)=X。
感覺也是很合理，可是我卡在第 (5) 結論這邊。
請問要怎麼解釋 sum x = x 這邊呢？
或者是我思考有錯？
謝謝大家指正。
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