In an office complex of 1100 employees, on any given day some are at work and the rest are absent. It is known that if an employee is at work today, there is an 80% chance that she will be at work tomorrow, and if the employee is absent today, there is a 51% chance that she will be absent tomorrow. Suppose that today there are 913 employees at work.

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In an office complex of 1100 employees, on any given day some are at work and the rest are absent. It is known that if an employee is at work today, there is an
80% chance that she will be at work tomorrow, and if the employee is absent today, there is a 51% chance that she will be absent tomorrow. Suppose that today
there are 913 employees at work.
.80
.49
( a) Find the transition matrix for this scenario.
.2
.51
(b) Predict the number that will be at work five days from now.
781.5
2.45
(c) Find the steady-state vector.
.29
Transcribed Image Text:In an office complex of 1100 employees, on any given day some are at work and the rest are absent. It is known that if an employee is at work today, there is an 80% chance that she will be at work tomorrow, and if the employee is absent today, there is a 51% chance that she will be absent tomorrow. Suppose that today there are 913 employees at work. .80 .49 ( a) Find the transition matrix for this scenario. .2 .51 (b) Predict the number that will be at work five days from now. 781.5 2.45 (c) Find the steady-state vector. .29
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