THE UNIVERSITY OF TEXAS AT AUSTIN
Department of Electrical and Computer Engineering
EE351K, Probability and Random Process, Fall 2007
Assignment No. 8; Due Thursday, October 25, 2007
1.
For the following joint pmf, find the following.
X
Y
1
2
2
3/8
1/8
3
2/8
2/8
(a)
Marginal pmf’s,
)
(
x
p
X
and
)
(
y
p
Y
(b)
Expected values,
]
[
X
E
and
]
[
Y
E
(c)
Variances,
]
[
X
V
and
]
[
Y
V
(d)
Conditional pmf’s,
)

(

y
x
p
Y
X
and
)

(

x
y
p
X
Y
(e)
Conditional expectations,
]

[
y
Y
X
E
=
and
]

[
x
X
Y
E
=
(f)
Are
X
and
Y
independent?
(g)
)
3
,
5
.
1
(
−
≥
≥
Y
X
P
(h)
)
3

0
(
=
≥
Y
X
P
(i)
Calculate
]
[
X
E
from
]

[
y
Y
X
E
=
.
(j)
Calculate
]
[
Y
E
from
]

[
x
X
Y
E
=
.
(k)
Calculate
]
,
[
Y
X
Cov
and
Y
X
,
ρ
.
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