Name:
Math 166 Quiz 13: M.1, M.2
Remember to show your work. Correct math is worth partial credit. Round to 4 decimal
places.
1. (2 points) Of doctor A’s patients, 85% will return to him again next year and 10% will go to
doctor B next time. Of doctor B’s patients, 23% will return next year and 1% will go to doctor
C. Of doctor C’s patients, 13% will return next year and 39% will go to doctor A. This year
6% of the patients went to doctor A, 84% of the patients when to doctor B, and 10% of the
patients went to doctor C. What is the transition matrix that describes this Markov process?
(2 points) What will be the distribution of patients in 2020?
(2 points) Is this a regular Markov process? If so, what is it’s steady state?
1
2. (2 points) Is
.25
.5
.25
0
1
0
1!
0
0
a regular stochastic matrix? Why or why not?
3. (2 points) Is
.25
.5
.65
0
1
.1
a regular stochastic matrix? Why or why not?
Page 2
1!
0
.25