EEE554 Assignment 4, Solution of problem (11.24)
(11.24) Determine
E
[(2
X
+ 1)
2
] for a
N
(
μ, σ
2
) random variable.
E
[(2
X
+ 1)
2
] =
E
[(2
X
+ 1)(2
X
+ 1)]
=
E
[4
X
2
+ 4
X
+ 1]
= 4
E
[
X
2
] + 4
E
[
X
] + 1
using linearity of expectation operator
= 4
E
[
X
2
] + 4
μ
+ 1
.
As variance is deFned as
σ
2
=
E
[
X
2
]

(
E
[
X
])
2
=
E
[
X
2
]

μ
2
, we can express
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This note was uploaded on 01/26/2011 for the course EEE 554 taught by Professor Duman during the Spring '10 term at ASU.
 Spring '10
 Duman

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