Question

7. The University of Wakanda has two residential dining halls, N'bomo and T'seki, which serve one meal daily. There are 600 students enrolled in a meal plan, who can choose where to dine. It has been observed that 20% of the students who eat at N'bomo on any given day switch to T'seki the following day, whereas 60% of students who eat at Tseki come back to T'seki. (Why? Who knows!) Campus Dining Services has decided to model the students' behavior by a Markov chain. a. (6 pt) Find the transition matrix. (10 pt) What percentage of the students dining in Tseki on a Tuesday will dine there again the following Friday? (12 pt) Estimate the daily number of diners at N'bomo in the middle of the academic term.

Answer 1

La liven: 20% of the students who eat at N'bomo on any given day switch T'seki the following day. : 100-20 = 80% students come back to N'bomo the following day. : From N'bomo Toy 80% ] N'bomo 20% ] Tseki • 60% of students who eat at T seki come back to T'seki : 100-60=40% of students switch to w'bomo the following day . From T'skki Tone 2017 N'bomo 6ot. Iseki transition matsix is . The required A= 801 201 404.7 Got =fo.8 10.2 such that I far where in 1h is the nth state vector. anty=1 (6) Let to represents the state rector on Tuesday Then i=107 N'bomo 1 ] T' Seki For Friday, n=3 {tuesday Wednesday Y = 45o = 10.8 0.411 -106 20.8 0.4110 10.32 +0241-10.567 Lo.2 0.6 lo. 10.08+0. 36 10.441 = Ar= 0.8 0.4780.5 10.4487 0.1761-10.624 .162.9%) - 10.2 0.6 /0.44) 10.112+02641 10. 3761 137.6% :: 37.6% of the students dining in Tseki on a Tursday will dine there again the following Friday