Neyman Pearson

[Sinistral]

I am bringing this problem again because I still have a few doubts:



Here is how I tried to solve:

f(xi)=[(1-p)^(1-xi)] * p^xi            ; xi=0,1

H0: p=p'=0
H1: p=p"=1/2
sample size is 2

L(p')/L(p")= 0/(1/4) =0 < k
since k is supposed to be a positive number ==> L(p')/L(p")< k for all Xis (here X1 and X2)

alpha = P_H0(X1=0,1 and X2=0,1) =0
beta= 1- P_H1(X1=0,1 and X2=0,1)
P_H1(X1=0,1 and X2=0,1) = P_H1(X1=0,X2=0) + P_H1(X1=0,X2=1) + P_H1(X1=1,X2=0) + P_H1(X1=1,X2=1)
                                    =(1/2)(1/2)*4 =1
beta= 1- P_H1(X1=0,1 and X2=0,1) = 1-1=0.
But both alpha and beta cant be zero.
someone please tell me how to apply neyman pearson in such cases.