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 = R, Mx(t) ≤ e²0²². 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¯ 20²2 (Hint: the method of proof of the one-sided Chebyshev inequality may provide some in- spiration.)

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