Midterm Examination
Ramesh Johari
February 11, 2009
Instructions
1. Take alternate seating if possible.
2. Answer all questions in the blue books provided. If needed, additional sheets of paper will
be available at the front of the room.
3. The examination begins at 11:00 am, and ends at 12:15 pm.
4. No notes, books, or calculators are allowed.
5. The exam will be scored out of 85 points.
6. Pace yourself!
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).
(Short answer)
Answer each of the following questions.
(a) (10 points) Suppose
{
X
n
}
is a Markov chain with transition matrix
P
. Further, suppose that
state
i
leads to state
j
, but that state
j
does not lead to state
i
.
True or false
: State
j
must be
transient. If true, explain why; if false, provide a counterexample.
(b) (10 points) Suppose
{
X
n
}
and
{
Y
n
}
are independent Markov chains. Consider a new random
process
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 Winter '11
 Ramesh
 Stochastic process, Markov chain, Andrey Markov, Ramesh Johari, Stanford University Honor Code

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