Question

in an office complex of 1090 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 81% chance that she will be at work tomorrow, and if the employee is absent today, there is a 61% chance that she will be absent tomorrow. ( a) find the stochastic matrix for this markov chain. let 'at work' come first in your ordering of rows / columns of . ( b) suppose there are 882 employees at work today. the predicted number of employees that will be at work five days from now is ( c) find the steady-state vector.

Answer 1

To construct the stochastic matrix for this Markov chain, determine the predicted number of employees at work five days from now, and find the steady-state vector, follow these steps.

Step-by-step explanation:

To construct the stochastic matrix for this Markov chain, we will use the information given.

Let's assume that the state 'at work' will be denoted by 1 and the state 'absent' will be denoted by 2. We can create the stochastic matrix using the transition probabilities given:

[0.81, 0.19]

[0.61, 0.39]

(b) To find the predicted number of employees that will be at work five days from now, we can multiply the current state vector by the stochastic matrix raised to the power of 5. Assuming the initial state vector is [882, 208], we get:

(882 * 0.81 + 208 * 0.61)5 = 485.8 employees.

(c) To find the steady-state vector, we need to solve the equation v = v * P, where v is the steady-state vector and P is the stochastic matrix. Solving this equation, we get the steady-state vector: [641.33, 448.67].