E[X|Y门的性质 10 定理：EE[XIY]=E[X] o证明：记E[X|Y]=f(Y) E[X IY]1=∑f)P(Y=) =∑EXIY=yPY=D=ELN刈𝑬 𝑿 𝒀]的性质  证明：记𝑬 𝑿 𝒀] = 𝒇 𝒀 𝑬[𝑬 𝑿 𝒀]] = ෍ 𝒚 𝒇 𝒚 𝑷 𝒀 = 𝒚 = ෍ 𝒚 𝑬 𝑿 𝒀 = 𝒚]𝑷(𝒀 = 𝒚) = 𝑬[𝑿] 10 定理：𝐸 𝐸 𝑋 𝑌 = 𝐸 𝑋