[理工] [機率]離散隨機變數

[nana0130 (小那)]

  The n   candidates for a job have been ranked 1,2,3,.....,n

  Let X = the rank of a randomly selected candidate , so that X has pmf

       1/n     x =1,2,3,....n
 p(x)=
        0      otherwiase

  Compute E(X)  and V(X) using the shortcut formula

  我有問題的是 E(X)

  E(X) = 1 * 1/1  +  2 * 1/2  + ......+ n * 1/n  = n

  為什麼答案是(n+1) /2 ??

  感謝高手幫忙，我的觀念真的不太熟~>"<

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◆ From: 140.116.39.115
→ CCWck:p(x)=1/n, not 1/x
→ nana0130:對阿~~ p(1) = 1 , p(2) = 1/2 不是嗎 ???
→ CCWck:全機率相加一定是1 你p(1)=1的話 怎麼還會有p(2)=1/2
→ kumafish07:E(x) = Σxf(x)=Σx*(1/n)=(1/n)*Σx=(1/n)*(1+n)*n/2
→ nana0130:感謝大家幫我解答QQ