DEPARTEMEN PENDIDIKAN NASIONAL UNIVERSITAS ANDALAS

FAKULTAS TEKNIK

JURUSAN TEKNIK INDUSTRI

LABORATORIUM PERENCANAAN DAN OPTIMASI SISTEM INDUSTRI

TUGAS SETELAH TUTORIAL

RANTAI MARKOV

1. A computer system can operate in two different modes. Every hour, it remains in the

same mode or switches to a different mode according to the transition probability

matrix

Compute the 2-step transition probability matrix.

2. Assume that a man’s profession can be classified as professional, skilled labourer, or

unskilled labourer. Assume that, of the sons of professional men, 80 percent are

professional, 10 percent are skilled labourers, and 10 percent are unskilled labourers.

In the case of sons of skilled labourers, 60 percent are skilled labourers, 20 percent are

professional, and 20 percent are unskilled. Finally, in the case of unskilled labourers,

50 percent of the sons are unskilled labourers, and 25 percent each are in the other two

categories. Assume that every man has at least one son, and form a Markov chain by

following the profession of a randomly chosen son of a given family through several

generations. Set up the matrix of transition probabilities. Find the probability that a

randomly chosen grandson of an unskilled labourer is a professional man.

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3. Customers in a certain city are continually switching the brand of soap they buy. If a

customer is now using brand A, the probability he will use brand A next week is 0.5,

that he switches to brand B is 0.2 and that he switches to brand C is 0.3. If he now

uses brand B, the probability he uses B next week is 0.6 and the probability that he

switches to C is 0.4. If he now uses brand C, the probability he uses C next week is

0.4, that he switches to A is 0.2 and to B is 0.4. Assume the process is a Markov Chain

(a) Find the probability a customer now using brand A will be using brand B in two

weeks.

(b) If the percentage of customers now using brand A is 30%, the percentage using brand

B is 20% and the percentage using brand C is 50%, find the percentage of customers

using brand C in three weeks. (c) Find the probability a customer now using brand A

will be using brand B in 6 weeks.

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