32. The following two examples show that the assumption of a finite sample space is needed in Problem 31. (i) Let Xl' " '' Xn be i.i.d. according to a normal distribution N( 0,02 ) and test H : 0 = 00 against K : 0 > 00 ' (ii) Let X and Y be independent Poisson variables with E( X) =.\ and E( Y) = .\ + 1, and test H:.\ =.\0 against K:.\ > .\0' In each case, determine the LMP test and show that it is not LUMP. [Compare the LMP test with the most powerful test against a simple alternative.]