EE 278
September 23, 2009
Statistical Signal Processing
Handout #1
Homework #1
Due: Wednesday September 30
You may either hand the assignment in class or drop it in the Homework In box
in the EE 278 drawer of the class file cabinet on the second floor of the Packard
Building by 5pm. Problems 1 and 2 are the bonus questions this week and you
can bet up to 10 points on each question.
1.
Monty Hall.
(Bonus)
Gold is placed behind one of three curtains. A contestant chooses one of
the curtains. Monty Hall, the game host, opens an unselected empty curtain. The contestant
can choose either to switch his selection to the third curtain or not.
a. What is the sample space for this random experiment?
Hint: an outcome consists of the
curtain with gold, the curtain chosen by the contestant, and the curtain chosen by Monty.
b. Assume that placement of the gold behind the three curtains is random, that the contestant’s
choice of curtains is random and independent of the gold placement, and that Monty Hall’s
choice of an empty curtain is equally likely between the two alternatives (if the two unselected
curtains are empty). Specify the probability measure for this random experiment and use it
to compute the probability of winning the gold if the contestant decides to switch.
2.
Conditional coin toss.
(Bonus)
Let
C
1
be an unbiased coin and let
C
2
be a biased coin with
probability of heads 3
/
4.
C
1
is tossed at time
t
= 0. If the result is heads, then
C
1
is tossed at
time
t
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 Fall '09
 BalajiPrabhakar
 Probability, Signal Processing, Probability theory, Monty Hall, Poisson approximation

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