2 Let X1Xn be a random sample from a distribution with pdf f

2. Let X1,...,Xn be a random sample from a distribution with pdf: fx(X/theta) = a. Show that T(bar X) = is a sufficient statistic for theta. b. Show that the family g(t/theta) for the statistic T, defined In part a, has an MLR. c. Derive a UMP level a test of H0: theta >= theta0 versus Ha: theta

Solution

a) It is sufficient because we do not have any other additional information.