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Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.7: Applications

Problem 18EQ

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Question

We say that a mean-zero random variable X is sub-Gaussian with parameter
o² if the m.g.f. of X satisfies, for all t ER,
Mx(t) ≤e ²0¹2
Let X be a sub-Gaussian random variable with parameter o². Using Markov's inequality,
show that, for all a > 0,
P(X ≥ a) ≤ e¯20²
(Hint: the method of proof of the one-sided Chebyshev inequality may provide some in-
spiration.)

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