Question

How to find mvue for a continuous random variable

Answer 1

Answer:

Let XX has probability density function fX(x;θ)=a(θ)b(x)I(0,θ)(x)fX(x;θ)=a(θ)b(x)I(0,θ)(x) (where a(θ)a(θ) and b(x)b(x) are nonnegative). I have to find the UMVUE of θθ or show that one doesn't exist. In a different part of the question, I showed that Y(n)Y(n) (the maximum of the X1,X2,...,XnX1,X2,...,Xn) is a complete sufficient statistic. I want to use Lehmann-Scheffe's theorem to find the UMVUE of θθ. I usually do this by first finding E(Y(n))E(Y(n)) then trying to find a function of Y(n)Y(n) with expectation equal to θ