23 A car rental agency at the three New York airports finds the likelihood that cars rented and returned to the various airports is given by the following table: Rented From Returned To Probability Kennedy LaGuardia Newark 80% 10% 10% Kennedy Kennedy LaGuardia Newark 30% 50% 20% LaGuardia Kennedy LaGuardia Newark 20% 50% 30% Newark

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
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Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 21PPS
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23 A car rental agency at the three New York airports finds the likelihood that cars rented and
returned to the various airports is given by the following table:
Rented From
Returned To
Probability
Kennedy
LaGuardia
Newark
80%
Kennedy
10%
10%
Kennedy
LaGuardia
Newark
30%
50%
20%
LaGuardia
Kennedy
LaGuardia
Newark
20%
50%
30%
Newark
Transcribed Image Text:23 A car rental agency at the three New York airports finds the likelihood that cars rented and returned to the various airports is given by the following table: Rented From Returned To Probability Kennedy LaGuardia Newark 80% Kennedy 10% 10% Kennedy LaGuardia Newark 30% 50% 20% LaGuardia Kennedy LaGuardia Newark 20% 50% 30% Newark
Consider the car rental and return as a Markov chain with Kennedy as state 1, LaGuardia
as state 2, and Newark as state 3. What is the two-step transition matrix for this chain (this
means two successive stages of car rentals)?
056 029 0.15
0.33 0.44 0.23
0.37 0.41 0.22
0.69 0.18 0.13
08 01 0.1
a)
0.35 0.42 0.23
b)
03 05 02
c)
0.40 0.38 0.22
02 0.5 03
0.69 0.18, 0.13
0.7 02 0.1
08 a1 0.1
d)
0.43 0.38 0.19
e)
02 0.5 03
f)
02 05 03
0.37 0.42 0.21
03 05 02
03 05 02
g) none of the others
Transcribed Image Text:Consider the car rental and return as a Markov chain with Kennedy as state 1, LaGuardia as state 2, and Newark as state 3. What is the two-step transition matrix for this chain (this means two successive stages of car rentals)? 056 029 0.15 0.33 0.44 0.23 0.37 0.41 0.22 0.69 0.18 0.13 08 01 0.1 a) 0.35 0.42 0.23 b) 03 05 02 c) 0.40 0.38 0.22 02 0.5 03 0.69 0.18, 0.13 0.7 02 0.1 08 a1 0.1 d) 0.43 0.38 0.19 e) 02 0.5 03 f) 02 05 03 0.37 0.42 0.21 03 05 02 03 05 02 g) none of the others
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