University of Illinois
Fall 2009
ECE 313:
Problem Set 6
Bayes’ Formula and Midterm Review Problems
Due:
Wednesday October 7 at 4 p.m.
Reading:
Powerpoint Lecture Slides, Sets 1316
Noncredit Exercises:
Chapter 3:
Problems 1, 2, 5, 10, 12, 16, 31, 38, 39, 51, 52
Theoretical Exercises 1, 2, 8, 16; SelfTest Problems 114.
Reminders:
No class on Wednesday September 30 and Friday October 2
but office hours as usual next week
1.
[Conditional Probabilities]
This is Theoretical Exercise 3.5 in Ross.
We say that event
B
gives
positive information
about event
A
if
P
(
A

B
)
> P
(
A
), that is, the
occurrence of
B
makes the occurrence of
A
more likely.
Now suppose that
B
gives positive information about
A
. If so,
(a) Does
A
give positive information about
B
?
(b) Does
B
c
give
negative information
about
A
, that is, is it true that
P
(
A

B
c
)
< P
(
A
)?
(c) Does
B
c
give positive information or negative information about
A
c
?
2.
[Hindsight]
The probability that a light bulb manufactured by Transylvania Corp. burns out during the
n
th hour
of operation is
p
1
(
n
),
n
= 1
,
2
,
. . . .
The probability that a light bulb manufactured by Eastinghouse
Corp. burns out during the
n
th hour of operation is
p
2
(
n
),
n
= 1
,
2
,
. . . .
Note that we are not giving
you numerical values of these probabilities but do not forget that
∑
p
1
(
n
) =
∑
p
2
(
n
) = 1.
A bulb is equally likely to have been made by one of the two manufacturers.
Express your answers to the following questions in terms of
p
1
(
n
) and
p
2
(
n
).
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 Spring '10
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 Probability, Probability theory, Alice, Alice and Bob

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