(11) Use the commonly stated form of Chebyshev's inequality to find an upper bound to P(X > 300) when X ~ - Poisson(10).
(11) Use the commonly stated form of Chebyshev's inequality to find an upper bound to P(X > 300) when X ~ - Poisson(10).
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
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Transcribed Image Text:(11) Use the commonly stated form of Chebyshev's inequality to find an upper bound to P(X > 300) when X - Poisson(10).
(a) Note that P(X > 300) = P(X > 300) + P(X< -300), since P(X < -280) = 0. So, we have
Std(X)
V10
P(X > 300) = P(|X| > 300) <
0.010540925.
300
300
(b) Note that P(X > 300) = P(X > 300) + P(X< -300), since P(X < -280) = 0. So, we have
Var(X)
10
P(X > 300) = P(|X|> 300)<
0.00011111.
3002
3002
(c) Cannot be done, since Chebyshev's inequality can only be applied when two sided tail probabilities are sought.
(d) Note that P(|X – 10| > 290) = P(X > 300) + P(X < -280), since P(X < -280) = 0. So, we have
Var(X)
10
P(X > 300) = P(|X – 10| > 290) <
0.000118906.
2902
2902
(e) None of the above.
The correct proof is
(а)
(b)
(c)
(d)
(e)
N/A
(Select One)
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