Let Xj, i = 1,2,... be i.i.d. continuous random variables that are uniformly distributed between [0,1]. Assuming x2 a) Provide a bound on PTEX;>x using Chebyshev and Markov inequalities. i=1 b) Use the central limit theorem approximation to provide an approximation (in terms of the o

Let Xj, i = 1,2,... be i.i.d. continuous random variables that are uniformly distributed between [0,1]. Assuming x2 a) Provide a bound on PTEX;>x using Chebyshev and Markov inequalities. i=1 b) Use the central limit theorem approximation to provide an approximation (in terms of the o

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.7: Applications

Problem 13EQ

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Let Xj, i = 1,2,... be i.i.d. continuous random variables that are uniformly distributed between [0,1].
Assuming x2
a) Provide a bound on
PREX;>x
using Chebyshev and Markov inequalities.
b) Use the central limit theorem approximation to provide an approximation (in terms of the o
function) for the expression in (a). In other words, provide an expression for
Pr EX;>x
i=1
using the central limit theorem.
c) Compute (a) and (b) for n = 50, and x = 80 and comment on your answers.

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