let X1,X2,...,Xn be a random sample from the uniformly distrubution. f(x)=1/θ θ<x<2θ , θ>0. Show that (1/2)Y1+(1/4)Yn is one mle of θ , where Y1,Y2,...Yn represent the order statistics of the random sample. 这是我们的做法 1 likelihood function is L(θ)=-----I[(1/2)Yn,Y1](θ) where I is indictor θ^n function. 明显的 L(θ)为一个θ递减函数 ,for all θ>0. 所以θ的mle为Yn 难以想像 为何(1/2)Y1+(1/4)Yn is one mle of θ ?? --

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