Show that the likelihood inequality in Theorem 17.3 holds for the Poisson distribution used in Section 17.3 by showing that E[(1/n) ln L( | y)]

Show that the likelihood inequality in Theorem 17.3 holds for the Poisson distribution used in Section 17.3 by showing that E[(1/n) ln L(θ | y)] is uniquely maximized at θ = θ0. Hint: First show that the expectation is −θ + θ0 ln θ − E0 [ln yi!].