Give the iid samples X 1 ,X 2 , . . . of X, define the sequence

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

Note that each Y_k is an example of VÊ¹₂, 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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Probability and Stochastic Processes A Friendly Introduction for Electrical and Computer Engineers

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Authors: Roy D. Yates, David J. Goodman

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Question Posted: Jul 18, 2016 08:46 AM

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Give the iid samples X 1 ,X 2 , . . . of X, define the sequence

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

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Note that we can write Y k as Hence E Y k 12 E X 2 2k 2X 2k X 2k1 X 2 2k1 E ...View the full answer

Probability and Stochastic Processes A Friendly Introduction for Electrical and Computer Engineers

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