This preview shows pages 1–5. Sign up to view the full content.
UCLA
EE131A (KY)
1
EE 131A
Probability
Professor Kung Yao
Electrical Engineering Department
University of California, Los Angeles
M.S. OnLine Engineering Program
Lecture 42
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document UCLA
EE131A (KY)
2
Conditional Probability is a Probability
P(
A

B
) satisfies all the axioms of probability.
Axiom I.
0
P(
A

B
) .
Axiom II.
P(
S

B
) = 1 .
Axiom III’. If
A
1
,
A
2
, …, are mutually exclusive (or
disjoint) (i.e.,
A
i
A
j
=
, for all i and j), then
ii
i=1
i=1
PP
.

AB
UCLA
EE131A (KY)
3
Conditional Probability (1)
Ex. 1.
Binary Symmetric Channel (
BSC
)
Consider the simplest model for a
binary
digital
communication
channel
for transmitting an input of
either an “0” or an “1.”
Denote A
0
for a channel input
of an “0” and A
1
for an input of an “1.”
The output can
be either an “0” or an “1.”
Denote B
0
for a channel
output of an “0” and B
1
for an output of “1.”
Since the
channel is imperfect (i.e., due to noise and other
disturbance), sending any A
i
, i = 0, 1, can result in any
B
j
, j = 0, 1.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document UCLA
EE131A (KY)
4
Conditional Probability (2)
Let the probability of receiving B
0
given A
1
was sent,
be denoted by the conditional probability
P(B
0
A
1
) =
,
(
~ small)
(1)
Probability of receiving B
1
given A
1
was sent becomes
P(B
1
A
1
) = P(B
0
C
A
1
) = 1 
.(
2
)
Channel is
symmetric
if prob. of receiving B
1
given A
0
P(B
1
A
0
) =
3
)
Then the probability of receiving B
0
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 11/05/2010 for the course ELECTRICAL EE131A taught by Professor Kungyao during the Spring '10 term at UCLA.
 Spring '10
 KungYao
 Electrical Engineering

Click to edit the document details