Probability and Stochastic
Homework 5
Solution
* Solutions of problems of Papoulis gathered from its Solution Manual
published by McGraw-Hill Higher Education.
1.
( )
( )
2.
3.
(
)
(
{
)
}
(
)
( )
(
)
4.
( )
(
(
)
(
(
[ (
)
)]
(
)
( (
)
)
( )
)( )
)
(
∑ (
[( )(
∑ (
)
(
))
(
(
∑ (
(
)( )
)
)(
(
)
)(
)
)]
)( )
(
)
(
(
) [(
) (
)
∑(
Assume:
( (
(
))
)
( (
( )
(
(
))
(
)
(
5.
∑(
)
)
)
(
)
)
)
(
)]
)
)(
)
6.
7.
8.
9.
10.
11.
( )
(
)
( )
∑( )(
)
(
)
∑ [( )
]
∑
12.
( )
∑
(
(
∑
(
∑
)
(
∑
)
)
)
∑
[
(
)
]
∑
(
)
∑
[
]