設總體X的概率密度為:f(x,θ)=e的[-(x-θ)]次方,x≥θ;0,x

設總體X的概率密度為:f(x,θ)=e的[-(x-θ)]次方,x≥θ;0,x

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左邊橫線在X上方)
其中 ̄X=1/n∑(從1到n)Xi