2. Let X₁, X2, X3,..., be independent identically distributed Unif(0, 1)random variables. Let Sn be the largest gap between any two of thepoints {X1, X2,..., Xn} (e.g. if n = 3 and (X₁, X2, X3) = (0.1, 0.5, 0.7)then S3 = 0.4). Show that for any x > 0lim P(nSn > x) = 1.n→∞Hint: to lower bound nSn > x, if suffices to demonstrate that thereis an empty interval of some length x/n which contains none of thepoints. Make a list of some candidate intervals and then use Cheby-shev's inequality to show one of them is empty with probability goingto 1.

Hint: Use Chebyshev's inequality for nSn>0.

Answered: Let X₁, X2, X3,..., be independent…

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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