Let X be a strictly positive r.v. with the following moment generating function:MX (t) = 1/(1 − 2t)^3(a) Use Markov’s inequality to find an upper bound for P (|X| ≥ 18).(b) Use Chebyshev’s inequality to find an upper bound for P (|X − 6| ≥ 12).(c) Find the lowest possible upper bound for P (X ≥ 18) you could get fromChernoff’s inequality.
Let X be a strictly positive r.v. with the following moment generating function:MX (t) = 1/(1 − 2t)^3(a) Use Markov’s inequality to find an upper bound for P (|X| ≥ 18).(b) Use Chebyshev’s inequality to find an upper bound for P (|X − 6| ≥ 12).(c) Find the lowest possible upper bound for P (X ≥ 18) you could get fromChernoff’s inequality.
A First Course in Probability (10th Edition)
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Let X be a strictly positive r.v. with the following moment generating function:
MX (t) = 1/(1 − 2t)^3
(a) Use Markov’s inequality to find an upper bound for P (|X| ≥ 18).
(b) Use Chebyshev’s inequality to find an upper bound for P (|X − 6| ≥ 12).
(c) Find the lowest possible upper bound for P (X ≥ 18) you could get from
Chernoff’s inequality.
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