(a) Find the sampling distribution of U in Problem 17.9 and graph it. (b) Graph the corresponding probability distribution of U. (c) Obtain the mean and variance of U directly from the results of part...

(a) Find the sampling distribution of U in Problem 17.9 and graph it.

(b) Graph the corresponding probability distribution of U.

(c) Obtain the mean and variance of U directly from the results of part (a).

(d) Verify part (c) by using formulas (3) of this chapter.

(e) If N numbers in a set are ranked from 1 to N, prove that the sum of the ranks is [N (N + 1)]/2.

(f) If R1 and R2 are the respective sums of the ranks for samples 1 and 2 in the U test, prove that R₁ + R₂ = [N(N + 1)]/2.