Question

Exercise 7.3.12 You own a trailer rental company in a large city and you have four locations, one in the South East, one in the North East, one in the North West, and one in the South West. Denote these locations by SE,NE,NW, and SW respectively. Suppose that the following table is observed to take place. SE NE NW SW SE C NE NW SW In this table, the probability that a trailer starting at NE ends in NW is 1/10, the probability that a trailer starting at SW ends in NW is 1/5, and so forth. Approximately how many will you have in each location after a long time if the total number of trailers is 1469 -1 -st t

Answer 1

Palobability taanstien Matain 1 P = 5 10 2 Let TT,, 2, T3 TT4 PRobabilities at these dapectively aftes oley time = 1 be the Jocation SE, NE Nw, Sw Hene 7T,+TT2+3 + 7 7T, 7T = TT2 4 PTT 7T atter long timce state balana eguation 777 3 TT3 5 TT 2. 4 4 16 . TTTT, + 4 2 4 lo -L -10 -n -d -1- mn- al --1N -F -7 MTM-t - 17 KEPK - /-mr 11

+ + T4 4 T2 TT2 3 + TT, ++ 72 4 +- TT3 T4 7 3 t T4 TT4 4 -TT2 + + 4 Rom and 2 T2+1 T42 T,- T2 IO 33 lo +T42T, T2 4 Rem and 3 =T3-TT, 11 2 -1L -4 -I2 +

and (4) 3 IT4= T4-T, 16 49 T4 90 16 bron 27 T, + 은.Yo으 TT, -2 T → 49 4 4 Io 49 284 T, 49 T2 TT2 4 245 We have T,+T2 +T3 TT4 = 245 1469 T1+ 245+ 2+ 90 284 =1 T 49 450 and T나 1469 490 hence 1T2284 1469T3 1469

Total tlailos ale 1469 Jeng ten Number of toniley Am the Cach Colner ale 1469 IT, 245 SE 1469 TT2 284 NE 490 1469 TT3 NW 1469 T4=450 SW