ECSE305, Winter 2009
Probability and Random Signals I
Assignment #1
Posted:
Tuesday, Jan. 13, 2009
Due:
Tuesday, Jan. 20, 2009, NO later than 2h30pm (please
use the assignment box)
Student #1:
Name:
ID:
Student #1:
Name:
ID:
Question
Marks
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Total
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1.
Let
A
=
{
1
,
2
, . . . ,
8
,
9
}
,
B
=
{
2
,
4
,
6
,
8
}
,
C
=
{
1
,
3
,
5
,
7
,
9
}
,
D
=
{
3
,
4
,
5
}
and
E
=
{
3
,
5
}
.
Which of the above sets, represented by
X
, satisfy the given conditions?
(a)
X
and
B
are disjoint;
(b)
X
⊆
D
but
X
*
B
;
(c)
X
⊆
A
but
X
*
C
;
(d)
X
⊆
C
but
X
*
A
.
2.
State whether the following sets are finite or infinite sets. If infinite,
specify if they are countable or uncountable.
(a)
A
=
{
all prime numbers
}
(b)
B
=
{
x
∈
R
: 0
< x <
10
}
(c)
C
=
{
x
∈
Q
: 0
< x <
10
}
(d)
D
=
{
x
∈
N
: 0
< x <
10
}
(e)
E
=
{
x
∈
N
:
x
2
= 10
}
3.
Show that each of the sets
A
∪
B
and
B
can be represented as a union
of mutually exclusive sets as follows:
A
∪
B
=
A
∪
(
B

A
)
and
B
= (
A
∩
B
)
∪
(
A
c
∩
B
)
Illustrate each situation by means of a Venn diagram.
4.
Consider the following sequences (i.e. indexed families) of intervals of
the real axis, where the index
i
∈
N
:
A
i
= (

1
i
,
1
i
)
,
B
i
= [

1
i
,
1
i
]
,
C
i
= (0
,
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 Spring '09
 Champagne
 Minibus, mutually exclusive sets, 2 bus

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