Re: [商管] [統計]-機率分配

[vity (拉麵愛吃辣椒)]

※ 引述《doremi987 (抖雷咪)》之銘言：
: The probability that the sum of 10 independent
: uniform (0,1) random variable exceeds 6 is approximalely?
: 請問一下這題要如何計算呢?
: 謝謝
Let r.v x~U(0,1)

Z = x - E(x) / [V(x)]^1/2

  = (x - 1/2) / (1/12)^1/2

Then,

x = (1/12)^1/2 * Z + 1/2

=> x1+x2+...+x10 = (1/12)^1/2 * 10Z + 5 ,where Z ~ N(0,1)

x1+x2+...+x10 ~ N(5, 10*(1/12)^1/2)


Answer = P(x1+...+x10 > 6)

       = P(Z > (6-5)/10*(1/12)^1/2)
       (check table)



不確定對不對
個人想法  供作參考


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