D
J
1
2
1
1
2
2
4
4
EE302 Homework #4


 


Hint:
Hint:
Hint:
Remark
X
X
i
i,
m
i
X
X
X
i
,
X
D
J
X
X
D
J
D
J
D
D
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J
D
J
( )
( ) = (1
) (1
)
(1
)
= 1
= 2
Pr (
)
(
)
( )
( ) = (1
)
= 1 2
Pr (
)
(
)
( ) = 0 5
0 25
2
2
( ) = 1
0 5
0 5
1 5
E
= 3
1
X
Y
X,
Y
X
p
i
p
i
p
p
p
p
i
, . . ., M
.
p
X > k
p
i X > k .
m
p
i
p
i
p
p
i
,
, . . ., .
p
X > k
p
i X > k .
X
X
f
x
.
.
x ,
< x <
.
f
x
x
.
,
.
< x <
. .
X
X
G
G
X
G
X
G .
X
X
X
X
X
.
R
Q
X
X
X
Assigned 2/21/10, Due 3/5/10 (by 4:30 in dropbox in MSEE 330)
1. Text, problem 3.42, page 134.
let
denote the number of heads. Then
is a linear
function of
and the mean and variance of
can be found in terms of the mean and variance
of
(the latter is a binomial random variable with mean and variance that can be found
from the text)
2. Text, problem 3.43, page 134.
for part (a)
can be written as
Determine what
is, and then evaluate
and
nally
3. Repeat problem 3.43 where the hacker forgets which patterns he has tested, and selects the
next pattern with equal probability from all of the
bit patterns.
for part (a)
can be written as
Determine what
is, and then evaluate
and
nally
4. Dwight and Jim are having a snowball
ght.
and
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 Spring '08
 GELFAND
 Normal Distribution, Variance, Probability theory, quantization error, Dwight s

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