# Science:Math Exam Resources/Courses/MATH152/April 2015/Question B 5 (a)

MATH152 April 2015
Other MATH152 Exams

### Question B 5 (a)

The percentage of people with the disease, March Madness, is recorded every week. Note that it is possible to recover from March Madness one week and catch it again the following week. Records indicate that the disease can be modelled by a random walk and that if 50% of the population is infected with March Madness one week, then 60% of the population will be infected the next week. Records also indicate that if 100% of the population is infected one week, then 90% of the population will be infected the next week. It is known that 10% of the population has March Madness this week.

(a) What is the ${\displaystyle 2\times 2}$ probability transition matrix for this system?
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