I would think that all n+m random variables are independent.
I would expect to see that the sample variances are
while the mean is a pooled estimator
Consider is a random sample from and is an independent random sample from
Let denote the joint distribution of these n+m variables with . Find a minimal sufficient statistics for this family of distributions.
My solution so far:
Now, we know that the joint density function for X and Y is:
First, since the Xi's are not independent, I'm not even sure if I can do this. Second, now I can't really compass my statistic , mainly to get the Xi's and Yj's together. Any hints? Thank you very much!