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EE 351K Probability, Statistics, and Random Processes
SPRING 2009
Instructor: Shakkottai/Vishwanath
{
shakkott,sriram
}
@ece.utexas.edu
Homework 1
Due Wednesday, Jan 28 2009 at 5pm
Problem 1
We are given that
P
(
A
) = 0
.
3
,
P
(
B
c
) = 0
.
45
, and
P
(
A
∪
B
) = 0
.
6
. Determine
P
(
B
)
and
P
(
A
∩
B
)
.
Problem 2
Let
A
and
B
be two sets.
(a) Show that
(
A
c
∩
B
c
)
c
=
A
∪
B
and
(
A
c
∪
B
c
)
c
=
A
∩
B
.
(b) Consider rolling a sixsided die once. Let
A
be the set of outcomes where a
3
or
4
comes up. Let
B
be
the set of outcomes where a prime number comes up. Calculate the sets on both sides of the equalities
in part (a), and verify that the equalities hold.
Problem 3
Alice and Bob each choose at random a number between zero and one. We assume a
uniform probability law under which the probability of an event is proportional to its area. Consider the
following events:
A: The magnitude of the difference of the two numbers is greater than
1
/
2
.
B: At least one of the numbers is greater than
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