Due 9/17: Chapter 2 Homework
1. Consider a sample space with five mem-
bers: 0, 1, 2, 3 and 4.
Assume the ELC
and i.i.d. trials. The following table helps
to visualize the results of the first two trials:
X
2
X
1
0
1
2
3
4
0
(0,0)
(0,1)
(0,2)
(0,3)
(0,4)
1
(0,1)
(1,1)
(1,2)
(1,3)
(1,4)
2
(0,2)
(2,1)
(2,2)
(2,3)
(2,4)
3
(0,3)
(3,1)
(3,2)
(3,3)
(3,4)
4
(0,4)
(4,1)
(4,2)
(4,3)
(4,4)
Define
X
=
X
1
+
X
2
, the total of the num-
bers obtained in the first two trials. Find the
sampling distribution of
X
.
2. Consider a sample space with three mem-
bers: 1, 2 and 3. Assume the ELC and i.i.d.
trials.
Define
X
=
X
1
+
X
2
+
X
3
, the total of
the numbers obtained in the first three tri-
als. Find the sampling distribution of
X
.
3. Consider a sample space with three mem-
bers: 1, 2 and 3. Do not assume the ELC.
Instead assume the following:
P
(1) = 0
.
4
, P
(2) = 0
.
2
and
P
(3) = 0
.
4
.
Assume i.i.d.
trials.
The following table
helps to visualize the results of the first two
trials:
X
2
X
1
1
2
3
1
(1,1)
(1,2)
(1,3)
2
(2,1)
(2,2)
(2,3)
3
(3,1)
(3,2)
(3,3)
Note that these nine entries are not equally
likely.
Define
X
=
X
1
+
X
2
, the total of the num-
bers obtained in the first two trials. Find the
sampling distribution of
X
.