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8. (a.) Let {Xn}neN be a sequence of independent random variables such that E(X₂) 0, E(X2) = 1 and E(|X₁|²+8) < M for some 8 > 0, M € R+ Vn N. Prove or disprove the following. 1 √Inn k=1 N(0, 1) (b.) Suppose now that {Xn}neN are iid with E(X) = 0, E(X2) = 1 and no additional re- strictions on higher order moments. Does the above convergence still hold?

8. (a.) Let {Xn}neN be a sequence of independent random variables such that E(X₂) 0, E(X2) = 1 and E(|X₁|²+8) < M for some 8 > 0, M € R+ Vn N. Prove or disprove the following. 1 √Inn k=1 N(0, 1) (b.) Suppose now that {Xn}neN are iid with E(X) = 0, E(X2) = 1 and no additional re- strictions on higher order moments. Does the above convergence still hold?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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8. (a.) Let {Xn}neN be a sequence of independent random variables such that E(Xn) 0, E(X²) = 1 and E(|X₁|²+6) < M for some > 0₁M € R+ \n € N. Prove or disprove the following. 1 Xk ✓ln n √k k=1 n ⇒ N(0, 1) = (b.) Suppose now that {Xn}neN are iid with E(X) = 0, E(X2) = 1 and no additional re- strictions on higher order moments. Does the above convergence still hold?
Transcribed Image Text:8. (a.) Let {Xn}neN be a sequence of independent random variables such that E(Xn) 0, E(X²) = 1 and E(|X₁|²+6) < M for some > 0₁M € R+ \n € N. Prove or disprove the following. 1 Xk ✓ln n √k k=1 n ⇒ N(0, 1) = (b.) Suppose now that {Xn}neN are iid with E(X) = 0, E(X2) = 1 and no additional re- strictions on higher order moments. Does the above convergence still hold?
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