Question

Question 3 4 pts An Uber driver provides service in city A and city B only dropping off passengers and immediately picking up a new one at the same spot. He finds the following Markov dependence. For each trip, if the driver is in city A, the probability that he has to drive passengers to city B is 0.25. If he is in city B, the probability that he has to drive passengers to city A is 0.45. Let the states be: 1 = "City A", and 2 = "City B". Find the following transition probabilities p_11 [Choose] p 12 [Choose ] p 21 [Choose] p_22 [Choose]

The options for each of options are either .25, .45, .75, or .55.

Answer 1

Ans. We have given a probabilities. - biz = 0.25 p21 = 0.45 Now, bu = 1- ki2 = 1- 0.25= 0.75 p22 ² 1 - bu - 0.45 - 0-55 3 Ane-4 The transition matrix is 10.75 bu bi 10.25 ) Co ) p22 0.45 10.55 Option c. is correct

Ans. 5 As we have given that the driver is in city B iso the initial probability be ) Xo = Co So, probability after trip 1: X = Xo. P = 6 lo 0-25 0.75 0.45 ) 0.55 (0.45 0-55) after trip 2: S. Now, probability X - X. P= 60-450-55)1.07 0.25 ) 0-55 0.45X0.25 +0.55 X0-55) (0-415X0-75 +0.55 X 0.45 = (0.585 0.415) (2) The required probability is bei = 0.585 option c is correct Note: 1. Herre 'P' denote the transition matrix 2. I had used this method. But there are many other way to get the answer. You can simply find the square of transition matrix ip pr and from that use pai as your required probability.

Anst For the steady-state distribution :- TP = T Where (TI T2) T 2 Ca T2 ) The Iron 0:25 (71. 0.45 0.55 2 T - 0.75 +0.45 T2 0-25 T t 0.55 72 We need to solve this equation along with 1 neimal equation, ie Tht Th = 1 from ep. 0 0.45 T2 = T (1-0.75) 0.45 TL2 = 0.25T, = 0.25T 1.8 T2 = TL = TI - 6 user Dance +48 Ietes Using ③ and 4 1.8 T12 + 2 = 1 2-8T12 z 1 T20-357 close As there is no option for our answer. But optim A is new very to our answer, so option A is correct.