In each of the following questions, you are given an i.i.d. sample and two hypotheses. For any

* 1 . ... . In ~ Poiss ( 1 ) for some unknown & > O'; HO : 1 = to v.s. HI : A * to where do > O. (Type bark_ n for *, lambda O for 10 . . If applicable , type abs ( x ) for |* 1 . Phi(x ) for $ ( x) = P ( Z O:` HO : 12 10 v.s. HI : A O . (Type bark_ n for*, lambda O for 10 . . If applicable , type abs ( x ) for | *1 . Phi(x ) for $ ( x) = P ( Z O . (Type bark_ n for* , lambda O for 10 . If applicable , type abs ( x) for |* 1 , Phi(x ) for $ ( x ) = P ( Z