A question on part C) and D) of problem 2:
It is asking us to find a distribution for which E(r(x)) will be less or more than the one under H* (Null hypothesis). But wouldn't E(r(x) depend on the parameters of a distibution? For example: E(r(x)) will be very big under H* if x ~ N(200,500) but will not be that big if x~N(0,1). So a uniform distribution from [0,1] may have smaller E(r(x)) than the later case of H* but may be larger than N(200,500) case.
Am I reading the problem wrong?
Thanks.