1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution So one of my assignments was to find a UMVUE of a Rayleigh distribution, that is the pdf f(x;θ)=2θ-1x*exp(-x2/θ). the suggestion was to use U=Ʃx2i. When I do this, I do a transformation with Ui=X2i and find that Ui has an exponential distribution, and the U=ƩUi follows a gamma(n,θ), so then n-1E(U)=θ, so then U-bar is the UMVUE of θ. I think this is correct. So then I am asked to see if it attains the CRLB, and I use the fact that U is Gam(n,θ) to show that yes indeed, it does reach the CRLB. All is well and good. Also, I'm asked to find the estimators of θ2 and θ-1, and find their variances. I did this, and it all relied on the fact that it was gamma distributed. On the next problem, I'm given that X follows a Weibull, that is, has the pdf f(x;θ)=α-1βxβ-1*exp(-xβ/α), where β (>0) is known, and it suggests starting off with U=ƩXβi. So when I make this transformation, I find the same thing, that Ui is exponential, so U=ƩXβi is distributed Gam(n,α). So here's why I'm confused. In both cases, I started with a pdf, transformed it to a different variable, but otherwise, finding the estimators and their variances aren't based on their original distribution, but the transformed distribution, which is the same. So I'd imagine that I just cut and paste my original work. It can't be that easy, right? What am I missing? The problems in the text are assigned right after each other, so... I'm assuming I'm wrong. Any help?