=+3.14. This problem is associated with Section 3.7.

(i) Verify that the LRT statistic is given by (3.21) and (3.22).

(ii) For fixed θ, consider the random variable Yi defined therein. Show that for any real number k, E(Y k i ) = exp k(k − 1)

2

θ2

.

It follows that E(Zi) = 0 and var(Zi) = eθ2

− 1, where Zi = Yi − 1.