# chap-9 - Chapter 9 Problems and Theoretical Exercises 1....

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139 Chapter 9 Problems and Theoretical Exercises 1. (a) P (2 arrivals in (0, s ) 2 arrivals in (0, 1)} = P {2 in (0, s ), 0 in ( s, 1)}/ e λ 2 /2) = [ e s ( s ) 2 /2][ e (1 s ) ]/( e 2 /2) = s 2 = 1/9 when s = 1/3 (b) 1 P {both in last 40 minutes) = 1 (2/3) 2 = 5/9 2. e 3 s /60 3. e 3 s /60 + ( s /20) e 3 s /60 8. The equations for the limiting probabilities are: c = .7 c + .4 s + .2 g s = .2 x + .3 s + .4 g g = .1 c + .3 s + .4 g c + s + g = 1 and the solution is: c = 30/59, s = 16/59, g = 13/59. Hence, Buffy is cheerful 3000/59 percent of the time. 9. The Markov chain requires 4 states: 0 = RR = Rain today and rain yesterday 1 = RD = Dry today, rain yesterday 2 = DR = Rain today, dry yesterday 3 = DD = Dry today and dry yesterday with transition probability matrix P = 8 . 2 0 0 2 . 8 .

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## This note was uploaded on 03/31/2008 for the course STAT 418 taught by Professor G.jogeshbabu during the Spring '08 term at Penn State.

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chap-9 - Chapter 9 Problems and Theoretical Exercises 1....

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