Rensselaer
Electrical, Computer, and Systems Engineering Department
ECSE4500 PEA
Final Exam
May 20, 2010
Closed book

two sheets of notes + calculator allowed
Please show work for full credit.
Only hand in your answer booklet
.
Good luck!
1. (10%) A fair die is tossed three times. Given that a 2 appears on the
fi
rst toss, what
is the probability of obtaining the sum 7 on the three tosses?
2. (10%) The average number of cars arriving at a tollbooth is
λ
cars per minute and the
probability of cars arriving is assumed to follow the Poisson law.
Given that 5 cars
arrive in the
fi
rst two minutes, what is the probability of 10 cars arriving in the
fi
rst 4
minutes?
3. (10%) Consider a communication channel corrupted by noise.
Let
X
be the value
of the transmitted signal and
Y
the value of the received signal.
Assume that the
conditional density of
Y
given
X
is Gaussian, that is,
f
Y

X
(
y

x
) =
1
√
2
πσ
2
exp
μ
−
(
y
−
x
)
2
2
σ
2
¶
,
and that
X
takes on only the values
+1
and
−
1
equally likely.
What is the conditional
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 Spring '11
 Radke
 Probability theory, Gaussian random variable, fY X, Laplacian random variable, conditional Gaussian density

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