推 hi123:請問為什麼可以推到F分配 ^^|| 12/26 07:32
題目:
Let X1, X2 ,…be independent continuous random variables with a common
distribution function F and density f = F', and suppose that they are to be
observed one at a time in sequence.
Let N = min{ n≧2: Xn = second largest of X1,…,Xn}
and let
M = min{ n≧2: Xn = second smallest of X1,…,Xn}
Which random variable ─ XN, the first random variable which when observed is
the second largest of those that have been seen, or XM, the first one that on
observation is the second smallest to have been seen ─ tends to be larger?
Sol:
這題書本上推導的結果是 XN 和 XM 的distribution都是 F
這題是要問 XN 和 XM which tends to be larger?
請問兩個隨機變數的分佈一樣 可以說他們一樣大嗎?
還是有其他的意義呢?
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