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Midterm Examination
Ramesh Johari
February 10, 2010
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 11:00 am, and ends at 12:15 pm.
4. No laptop computers or other networked devices are allowed, but you may use any other
nonhuman aids you wish.
5. The exam will be scored out of 50 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 (12 points).
Suppose
X
0
, X
1
, X
2
, . . .
is a sequence of i.i.d. Bernoulli random variables, with
P
(
X
n
= 0) =
P
(
X
n
= 1) = 1
/
2
.
(a) (6 points) For
n
≥
1
, define
Y
n
=
X
n
+
X
n

1
. Is
Y
1
, Y
2
, Y
3
, . . .
a Markov chain? Explain
your answer.
(b) (6 points) Suppose
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 Winter '11
 Ramesh

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