(1 point) Note: In this problem, use the method you learned in this week\'s tuto

Question

(1 point) Note: In this problem, use the method you learned in this week's tutorial. You can find the tutorial worksheet on Brightspace. In an office complex, on any given day some employees are at work and the rest are absent. It is known that if an employee is at work today, there is a 75% chance that she will be at work tomorrow, and if the employee is absent today. there is a 45% chance that she will be absent tomorrow. (a) Find the probability matrix for this scenario. Make your first column/row about being at work and your second column/row about being absent 0.75 0.55 0.25 0.45 (b) If an employee was at work today, what is the probability that she will be at work two days from now? 0.7 (c) Find the steady-state vector 0.5 0.5

Explanation / Answer

solution:
The matrix can be constructed as follows

b. now, the proabibility of being at work for 2 days would be 0, since he was at work today,
0.75*0.75= 0.56

c) Let the steady state probabilities for 2 states be X and Y , X for working and Y for absent.

Then from first column of the transition matrix we get:

X = 0.75X + 0.55Y

0.25 X = 0.55 Y

X = 2.2 Y

Also sum of the 2 probabilities should be equal to 1, Therefore we get:

X + Y = 1

2.2 Y + Y = 1

3.2 Y =1

Y = 0.3125

X = 0.6875

Therefore the steady state probabilities are :

( 0.6875 , 0.3125 )

Thumbs up if this was helpful, otherwise let me know in comments

day 2 day 1 present absent present 0.75 0.25 absent 0.45 0.55

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