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Unformatted text preview: 7.5% in 1990, and 59.8% in 2000. In
the long run what fraction of women will be working?
1.19. A rapid transit system has just started operating. In the ﬁrst month of
operation, it was found that 25% of commuters are using the system while 75%
are travelling by automobile. Suppose that each month 10% of transit users go
back to using their cars, while 30% of automobile users switch to the transit
system. (a) Compute the three step transition probaiblity p3 . (b) What will
be the fractions using rapid transit in the fourth month? (c) In the long run? 66 CHAPTER 1. MARKOV CHAINS 1.20. A regional health study indicates that from one year to the next, 75%
percent of smokers will continue to smoke while 25% will quit. 8% of those
who stopped smoking will resume smoking while 92% will not. If 70% of the
population were smokers in 1995, what fraction will be smokers in 1998? in
2005? in the long run?
1.21. Three of every four trucks on the road are followed by a car, while only
one of every ﬁve cars is followed by a truck. What fraction of vehicles on the
road are tru...
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This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell University (Engineering School).
 Spring '10
 DURRETT
 The Land

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