8. (Continued from HW10, #1) Consider a random sample from the distribution f(x) = x2 , x . We wish to test H0 : 0 vs H1 : > 0. Derive a formula for the P-value based on the observed test statistic value T.

(HW10 #1. Consider a random sample from the distribution f(x) = x2 , x . We wish to test H0 : 0 vs H1 : > 0. (a) Show that this distribution is MLR in the sufficient statistic T. (b) Find the form of the UMP size- test. (c) Express a formula for t0 in terms of , n, and 0.)