A family of random variables {X, E [a, b]} is said to be a monotone likelihood ratio family if X, LR X, when 0, 02. Show that the follow- ing families have monotone likelihood ratio

(a) X, is binomial with parameters n, 0, n fixed.

(b) X, is Poisson with mean

(c) X, is uniform (0, 0)

(d) X, is gamma with parameters (n, 1/0), n fixed

(e) X, is gamma with parameters (0, ), A fixed