If X 1¦ X n are i.i.d. r.v.s with ÉX 1 = μ R and Ï 2

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If X1€¦ Xnare i.i.d. r.v.s with É›X1= μ ˆˆ R and σ2(X1) = σ2ˆˆ (0, ˆž), then (by Application 2 to Theorem 9 in this chapter) it follows that

Sn-nu > Z ~ o yn n-00

N(0,1) Where

If X1... Xn are i.i.d. r.v.s with ɛX1 = μ

Show that

If X1... Xn are i.i.d. r.v.s with ɛX1 = μ

Does not converge in probability as n †’ ˆž

Set Yn = (Sn €“ nμ)/σˆšn and show that, as n †’ ˆž, (Yn) does not converge mutually in probability by showing that [Y2n - Yn] does not converge in probability to 0.

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