EEL 5544 Midterm Examination Number 2
December 1, 2010
The time for this test is 2 hours. This is a closed book test, but you are allowed two formula
sheets. The formula sheets cannot contain any examples. You should
write your name on the
formula sheets
and turn them in with your exam. You may use a calculator on this test. You must
show your work to receive credit for a problem. Note that some problems are worth more points
than other problems, and the problems are not necessarily sorted in order of difficulty or point
value. You must sign the honor statement at the end of the test in order to receive any credit.
Some potentially useful facts:
Best Linear MMSE Estimator for
X
given
Y
ˆ
X
=
ρσ
X
σ
Y
(
Y

μ
Y
)+
μ
X
Best MMSE Estimator for
X
given
Y
ˆ
X
=
E
[
X

Y
]
Bivariate Gaussian density
f
X
,
Y
(
x
,
y
)
=
1
2
πσ
X
σ
Y
1

ρ
2
X
,
Y
exp

1
2
(
1

ρ
2
X
,
Y
)
x

μ
X
σ
X
2

2
ρ
X
,
Y
x

μ
X
σ
X
y

μ
Y
σ
Y
+
y

μ
Y
σ
Y
2
For the Poisson Random variable,
μ
=
σ
2
.
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 Spring '11
 Wang
 Probability theory, Chernoff

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