In a city three factories X, Y, Z in which the number of workers in total is a fixed number. However, it is allowed to shift from one factory to another in each month and the scenario is described in percentage as follows. At the end of each month 30% move from X to Y, 20% move from X to Z rest stay in X, 20% move from Y to X, 30% move from Y to Z, rest stay in Y, 30% move from Z to X, 35% move Z to Y, rest stay in Z. Draw the transition diagram and write the Transition matrix. If initially in the first month the state vector is given by x0-[50, 45, 35], then what is the situation in the second month? Also find the steady state vector

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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In a city three factories X, Y, Z in which the number of workers in total is a fixed
number. However, it is allowed to shift from one factory to another in each month
and the scenario is described in percentage as follows. At the end of each month
30% move from X to Y, 20% move from X to Z rest stay in X, 20% move from Y
to X, 30% move from Y to Z, rest stay in Y, 30% move from Z to X, 35% move Z
to Y, rest stay in Z. Draw the transition diagram and write the Transition matrix. If
initially in the first month the state vector is given by x0-[50, 45, 35], then what is
the situation in the second month? Also find the steady state vector
Transcribed Image Text:In a city three factories X, Y, Z in which the number of workers in total is a fixed number. However, it is allowed to shift from one factory to another in each month and the scenario is described in percentage as follows. At the end of each month 30% move from X to Y, 20% move from X to Z rest stay in X, 20% move from Y to X, 30% move from Y to Z, rest stay in Y, 30% move from Z to X, 35% move Z to Y, rest stay in Z. Draw the transition diagram and write the Transition matrix. If initially in the first month the state vector is given by x0-[50, 45, 35], then what is the situation in the second month? Also find the steady state vector
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