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HW11New-Sol

HW11New-Sol - Markov inequality gives P X> 85 ≤ E X 85...

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EE/NIS 605-CS505 Probability and Stochastic Processes I Homework 11 Textbook: S. Ross, A First Course in Probability, Seventh Edition , Prentice Hall, 2006 Chapter 8 : P1: P [0 < X < 40] = P [| X – 20| < 20] =1 – P [|| X – 20| >20] > 1 – σ 2 (20) 2 = 1 – 20 400 = 0.95 where we have used the Chebyshev inequality. P2a:
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Unformatted text preview: Markov inequality gives P [ X > 85] ≤ E [ X ] 85 = 75 85 = .8823 P4b: Standardizing the summation and using the central limit theorem gives the approximation P [ X i Σ i = 1 20 > 15] = P [ X i Σ i = 1 20 – 20 20 > – 5 20 ] ≈ φ (1.1) = .8643 Professor Heffes...
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