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Unformatted text preview: u can pick up bikes at the library (L), the co↵ee shop (C) or the cooperative
grocery store (G). The director of the program has determined that bikes move
around accroding to the following Markov chain
L
C
G L
.5
.4
.25 C
.2
.5
.25 G
.3
.1
.5 On Sunday there are an equal number of bikes at each place. (a) What fraction
of the bikes are at the three locations on Tuesday? (b) on the next Sunday?
(c) In the long run what fraction are at the three locations?
1.31. A plant species has red, pink, or white ﬂowers according to the genotypes
RR, RW, and WW, respectively. If each of these genotypes is crossed with a
pink (RW ) plant then the o↵spring fractions are
RR
RW
WW RR
.5
.25
0 RW
.5
.5
.5 WW
0
.25
.5 What is the long run fraction of plants of the three types?
1.32. The weather in a certain town is classiﬁed as rainy, cloudy, or sunny and
changes according to the following transition probability is
R
R 1/2
C 1/4
S 1/2 C
S
1 / 4 1 /4
1/2 1/4
1/2
0 In the long run what proportion of days in this town are rainy? cloudy? sunny?
1.33. A sociologist studying livin...
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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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