2. Let X1,X2, . . . ,Xn be a random sample from logistic PDF f(x) = 1 2[1+cosh(x)] = ex {1+ex}2 . Show that the

2. Let X1,X2, . . . ,Xn be a random sample from logistic PDF fθ(x) =

1 2[1+cosh(x−θ)]

=

ex−θ

{1+ex−θ}2 .

Show that the LMP test of H0 :θ=0 against H1 :θ>0 rejects H0 if

n

% i=1 tanh xi 2

&

> k.