EE 562a Midterm Exam B SOLUTIONS, 28 Februrary 2007
WRITE YOUR NAME on the exam paper, and indicate if you are an ONCAMPUS or DEN
student. The exam is open book/open notes. You may use a simple calculator (i.e., not a scientific
calculator).
Do all problems.
Note that these problems have different point values, and differ widely in
difficulty. You should look over all the problems before starting your work.
Write all answers on
the test paper.
You may use scratch paper to do the problem, but the answer must be written
with the problem on the exam paper. If you do work on scratch paper, and wish that work to be
considered for partial credit, hand in the scratch paper along with the exam.
Part I. Basic Concepts.
For each question in this section, circle the best answer from the choices listed. Each problem has
only one best answer. There is no partial credit on this section. (3 points each.)
1. Suppose
x
(
u
) and
y
(
u
) are jointly Gaussian real random vectors.
Which of the following
gives enough information to find their joint probability density function?
(a)
R
x
and
R
y
(b) R
x
, R
y
, m
x
, m
y
, and that x
(
u
)
and y
(
u
)
are uncorrelated
(c)
K
x
,
K
y
,
m
x
and
m
y
(d)
R
x
,
K
y
,
m
y
, and that
x
(
u
) is meanzero
2. Which of the following is an affine transformation?
3. Suppose that a circular random
d
vector
x
(
u
) has a
d
×
d
covariance matrix with rank
r < d
.
Which of the following is possible by an affine transformation?
4. Which of the following could be allowed as a preprocessing step without loss of information
(with no restriction on the type of allowed operations)?
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 Spring '07
 ToddBrun
 Variance, Probability theory, Midterm Exam Solutions, KXX

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