Question

Suppose $X_{1},...,X_{n}$ is a random sample from $N(\theta ,\theta )$ , where $V(X_{i})=\theta$ and $\sqrt{\theta }>0$ .

(a) Find a minimal sufficient statistic for $\theta$.

(b) Find a complete statistic for $\theta$.

(c) Show that $n^{-1}\sum_{i=1}^{n}X_{i}^{2}$ is independent of $\frac{\bar{X} - X_{1}}{S}$ , where $S^{2}=(n-1)^{-1}\sum_{i=1}^{n}(X_{i}-\bar{X})^{2}$ .

Answer 1

the following two images have the solution with explanations...so check them out!!

image 1:

29 n/2 2-0) 2 20 二e Oxi a beue uwit be foe

image 2:

So o's Tene houe that of des t2 Jo indekindent

thats all...do thumbs up this helped

good luck :)