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Midterm Examination
Ramesh Johari
February 13, 2006
Instructions
1. Take alternate seating if possible.
2. Answer all questions in the spaces provided on these sheets. If needed, additional paper will
be available at the front of the room. Answers given on any other paper will not be counted.
3. The examination begins at 1:05 pm, and ends at 2:15 pm.
4. No notes, books, or calculators are allowed.
5. The exam will be scored out of 150 points.
6. Pace yourself! Note that part 2(f) and part 3(e)(f) are harder than the rest of the exam, and
you should leave them for last.
Honor Code
In taking this examination, I acknowledge and accept the Stanford University Honor Code.
NAME
(signed)
NAME
(printed)
1
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View Full DocumentProblem 1 (40 points).
Answer each of the following questions TRUE or FALSE. If TRUE, provide a brief justification
(12 sentences) for your answer; if FALSE, provide a brief counterexample. (5 points per correct
answer; 5 points per correct justification/counterexample)
(a) Every Markov chain with a finite state space has at least one closed class.
(b) Every Markov chain on a finite state space with a symmetric transition matrix has an invariant
distribution. (A matrix is
symmetric
if
A
ij
=
A
ji
for all
i,j
.)
2
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 Winter '11
 Ramesh

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