Principles of Digital Communications
EPFL Summer Semester 2007
April 26, 2007
Midterm
This is a closedbook exam, but a single page of handwritten notes is allowed. Cal
culators and cellphones are not allowed.
You have 1 hour 45 minutes to solve the problems.
Try to do side calculations on a separate sheet and report well organized solutions.
If we can’t read it we can’t grade it.
If you need additional pages, do not forget to write your name!
Good Luck!!
Name:
Problem 1
/ 13
Problem 2
/ 5
Problem 3
/ 6
Problem 4
/ 11
Total
/
35
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
1.
Bhattacharyya Bound
(13 points)
When
Y
∈
R
is an continuous random variable, the Bhattacharyya bound
states that
Pr
{
Y
∈ B
i,j

H
=
i
} ≤
radicalBigg
P
H
(
j
)
P
H
(
i
)
integraldisplay
y
∈
R
radicalBig
f
Y

H
(
y

i
)
f
Y

H
(
y

j
)
dy,
where
i, j
are two possible hypotheses and
B
i,j
=
{
y
∈
R
:
P
H
(
i
)
f
Y

H
(
y

i
)
≤
P
H
(
j
)
f
Y

H
(
y

j
)
}
. In this problem
H
=
{
0
,
1
}
and
P
H
(0) =
P
H
(1) = 0
.
5.
(a) (2 points) Write a sentence that expresses the meaning of
Pr
{
Y
∈ B
0
,
1

H
=
0
}
. (You may write in English or French. Use words that have operational
meaning.)
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '09
 IzhakRubin
 Probability distribution, Probability theory, probability density function, YS

Click to edit the document details