Please answer with steps 2. Joe loves to eat out in area restaurants. His favori

Question

Please answer with steps
2. Joe loves to eat out in area restaurants. His favorite foods are Mexican, Italian, Chinese, and thai. On an average, joe pays $10.00 FOR Mexican meal, $15.00 for Italian meal, $9.00 for a Chinese meal, and $11.00 for a Thai meal. Joe's eating habits are predictable: There is 70% chance that today's meal is a repeat of yesterdays, and equal probabilities of switching to one of the remaining three. a. How much does Joe, pay on the average for his daily dinner? b. How often does Joe eat Mexican food?

Explanation / Answer

a) Transition Matrix

solve for steady state
M = 0.7M + 0.1I + 0.1C + 0.1T
I = 0.1M + 0.7I + 0.1C + 0.1T
C = 0.1M + 0.1I + 0.7C + 0.1T
T = 0.1M + 0.1I + 0.1C + 0.7T
M + I + C + T = 1

Solving we get, M = 1/4, I = 1/4, C = 1/4, T = 1/4

Mean = 0.25*10 + 0.25*15 + 0.25*9 + 0.25*11 = $11.25

b) Joe eats Mexican food 25% of the time

M I C T M 0.7 0.1 0.1 0.1 I 0.1 0.7 0.1 0.1 C 0.1 0.1 0.7 0.1 T 0.1 0.1 0.1 0.7

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