In the definition of wilcoxons statistic let w1 be the sum, Ask an Expert

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In the definition of Wilcoxon's statistic, let W1 be the sum of the ranks of those observations of the sample that are positive and let W2 be the sum of the ranks of those observations that are negative. Then W = W1 - W2.

(a) Show that W = 2 W1 - n( n + 1)/2 and W = n( n + 1)/2 - 2 W2.

(b) Compute the mean and the variance of each of w, and, .w2.

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