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 LMP test of H0 0 against H1 0 rejects H0 if n i 1 tanh xi 2 k ...

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2. Let X1,X2, . . . ,Xn be a random sample from logistic PDF f(x) = 1...

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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

% i=1 tanh xi 2

> k.

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