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Unformatted text preview: 1 n ↓ 1 where P 1 2 = 0. (v) Show that there exists an F ∞measurable random variable Z for which X n → Z almost surely. (vi) Show that Z = X ∞ almost surely. (vii) ±or each n , show that X n = P ( X ∞  F n ) almost surely. Hint: Read UGMTP §6.6. *(11.3) (branching process, µ > 1, σ 2 < ∞ ) UGMTP Problem 6.13. (11.4) (second moment SLLN via martingales) UGMTP Problem 6.15. (Kronecker’s lemma is given in UGMTP Problem 4.22. There is no need to prove it.) (11.5) (densities via martingales) UGMTP Problem 6.10....
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This note was uploaded on 11/21/2009 for the course STAT 330 taught by Professor Davidpollard during the Spring '09 term at Yale.
 Spring '09
 DavidPollard
 Statistics, Probability

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