Let Xi be independently distributed as N(i∆, 1), i = 1,...,n.

Show that there exists a UMP test of H : ∆ ≤ 0 against K : ∆ > 0, and determine it as explicitly as possible. Note. The following problems (and some of the Additional Problems in later chapters) refer to the gamma, Pareto, Weibull, and inverse Gaussian distributions. For more information about these distributions, see Chapter 17, 19, 20, and 25 respectively of Johnson and Kotz (1970).