Consider the following transition probability matrix: [0.6 0.2 0.2 P= 0.3 0.4 0.3 0.0 0.3 0.7 a. Give the state-transition diagram. b. Given that the process is currently in state 1, what is the probability that it will be in state 2 at the end of the third transition? c. Given that the process is currently in state 1, what is the probability that the first time it enters state 3 is the fourth transition?

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.EA: Extended Application Using Extrapolation To Predict Life Expectancy
Problem 8EA
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12.43 Consider the following transition probability matrix:
0.6 0.2 0.2
P= 0.3 0.4 0.3
0.0 0.3 0.7
a. Give the state-transition diagram.
b. Given that the process is currently in state 1, what is the probability
that it will be in state 2 at the end of the third transition?
c. Given that the process is currently in state 1, what is the probability
that the first time it enters state 3 is the fourth transition?
Transcribed Image Text:12.43 Consider the following transition probability matrix: 0.6 0.2 0.2 P= 0.3 0.4 0.3 0.0 0.3 0.7 a. Give the state-transition diagram. b. Given that the process is currently in state 1, what is the probability that it will be in state 2 at the end of the third transition? c. Given that the process is currently in state 1, what is the probability that the first time it enters state 3 is the fourth transition?
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