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

If X_1€¦ X_nare 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

N(0,1) Where

Show that

Does not converge in probability as n †’ ˆž

Set Y_n = (S_n €“ nμ)/σˆšn and show that, as n †’ ˆž, (Y_n) does not converge mutually in probability by showing that [Y_2n - Y_n] does not converge in probability to 0.

Transcribed Image Text:

Sn-nu > Z ~ o yn n-00