(a)(b)Two independent random variables X, Y have zero mean, and variance 3, 6respectively. Estimate how large a > 0 has to in order to haveP(|X + Y≥ a) ≤100·?Let X be a nonnegative random variable with moment generating functionMx(X) = eH(X), H: [0, ∞) → [0, ∞).Suppose it holds for all λ, t > 0 that λt – H(X) ≥ G(t). Prove:P(X > t) ≤ e-G(t).

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Answered: (a) Two independent random variables X,…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.CR: Chapter 13 Review

Problem 1CR

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(a) Two independent random variables X, Y have zero mean, and variance 3,6 respectively. Estimate how large a > 0 has to in order to have P(|X+Y| ≥ a) ≤ 1 -? 100