Give the iid samples X₁,X₂, . . . of X, define the sequence Y₁,Y₂, . . .by

Note that each Y_k is an example of Vʹ₂, an estimate of the variance of X using two samples, given in Theorem 10.13. Show that if E[X^k] < ˆž for k = 1,2,3,4, then the samples mean M_n (Y) is a consistent , unbiased estimate of Var[X].

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X2k-1 + X2k X2k-1 = ( X2k-1 Yk