[機統] correlation

[debdeb ()]

       Let X1,...,Xn be a iid sample from a distribution F(x), and let

               1   n
       Fn(x)= ----Σ   I         (Xi), where
               n  i=1   (-∞, x]

                        1   if Xi<= x
       I        (Xi) =
        (-∞, x]        0   if Xi> x

       Find the correlation of Fn(u) and Fn(v).


   　　麻煩指點一下，謝謝！！

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◆ From: 218.171.162.113
→ yhliu       :Cov(Fn(u),Fn(v))=E[Fn(u)Fn(v)]-E[Fn(u)]E[Fn(v)]
→ debdeb      :謝謝，不過我就是卡在E[Fn(u)Fn(v)]這裡
→ debdeb      :請問兩個summation要怎麼乘？
→ yhliu       :乘開, 計算 E[I_(-∞,u](X_i)I_(-∞,v](X_j)] 時分
→ yhliu       :i=j 與 i=/=j 兩種情況.