设总体X的概率密度为：f(x,θ)=e的[-(x-θ)]次方,x≥θ；0,x

题目

设总体X的概率密度为：f(x,θ)=e的[-(x-θ)]次方,x≥θ；0,x

答案

EX=∫(上+∞下θ)xf(x,θ)dx=∫(上+∞下θ)xe^[-(x-θ)]dx
=-(xe^[-(x-θ)]|(上+∞下θ)-∫(上+∞下θ)e^[-(x-θ)]dx)
=-θ-1=µ
θ=-µ-1
θ^=-￣X-1(X左边横线在X上方)
其中￣X=1/n∑(从1到n)Xi