2. Let {Xn}n>1 be a sequence of random variables ón somê probability space su that (a) EX? < 0, i > 1; (b) E(X;X;) = E(X;)E(X;), i # j; (c) -1 % → 0, as n → 0, where of = var(Xx). Then for X, = E X;/n and ūn = LE(X;), show %3D Xn - in n → 0. as
2. Let {Xn}n>1 be a sequence of random variables ón somê probability space su that (a) EX? < 0, i > 1; (b) E(X;X;) = E(X;)E(X;), i # j; (c) -1 % → 0, as n → 0, where of = var(Xx). Then for X, = E X;/n and ūn = LE(X;), show %3D Xn - in n → 0. as
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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Transcribed Image Text:Let {Xn}n>1 be a sequence of random variables on some probability space such
that
(a) EX? < o, i > 1;
(b) E(X;X;) = E(X;)E(X;), i ± j;
(c) C-1 % → 0, as n → co,
-k%3D1°K
where of = var(Xx). Then for X, = C, X;/n and ūn = CE(X;), show
k
X, – in
as n → o.
2.
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