Edited by author 10-14-2002 09:59 PM
hi,
I am at my wit's end about 2.6 and now I think I have found a counterexample. I would appreciate if someone could pointout where I am wrong.

consider the normal N(\mu,\sigma^2)

when \mu is known a sufficent statistic for \sigma is
t_1 = \sum_i (x_i -\mu)^2

and when \sigma is known, a sufficent statistic for \mu is

t_2 = \sum_i x_i

the pair (t_1,t_2), depends on \mu and I see no way of eliminating it, once we are given expressions for t_1, and t_2, since the problem does not place any restrictions on the form of the sufficent statistics, (t_1,t_2) should now be a sufficent statistic for (\sigma^2,\mu), which is not true.

what am I missing ?