Question: Statistic Gk, defined for k = 1, 2 as Gk = 1 n(n 1) n i=1 n j =1 |Xi Xj | k,

Statistic Gk, defined for k = 1, 2 as Gk = 1 n(n − 1)

n i=1 n

j =1

|Xi − Xj |

k, was proposed as a measure of variation by Jordan (1869). Show that G2 = 2S2, where S2 is given by formula (9.1).

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