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# Markov Chain problems

In a large metropolitan area, 23% of the commuters currently use the public transportation system, and the rest commute via automobile. The city has recently revitalized and expanded its public transportation system. It is expected that 6 months from now 31% of those who are now commuting to work via automobile will switch to public transportation. At the same time, it is expected that 19% of those now using public transportation will commute via automobile. The rest will just continue to commute as they are now.

1.What percentage of the commuters are expected to use public transportation 6 months from now?

2.If the switching trend continues, what percentage of the commuters are expected to use public transportation 12 months from now?

3.In the long run, what percentage of the commuters will be using public transportation

4.Part-time students in a university MBA program are considered to be first-year students until they complete 15 credits successfully. Then they are classified as second-year students and can take more advanced courses and work on the thesis required for graduation.Past records indicate that at the end of each year, 11% of the first-year students (F) drop out of the program (D) and 34% become second-year students (S). Also, 8% of the second-year students drop out of the program and 35% graduate (G) each year. Students who graduate or drop out never return to the program.

If 200 students have just entered this MBA program, estimate

how many of them will graduate within 2 years?

### 2 個解答

• 6 年前
最愛解答

If you can wait, you should extend the question and I will do it in the weekend.

Q3 is just solving the vector from the TPM (transition probability matrix) with the standard method, not hard.

I suggest that you read Ross's textbook "Introduction to Probability Models".

2015-03-31 19:33:39 補充：

You are welcome.