STAT 400
Spring 2011
Homework #6
(due Friday, March 4, by 3:00 p.m.)
From the textbook:
8th edition
(
)
1.
3.32 (a)
,
3.34 (a)
(
,
)
2.
3.32 (b)
,
3.34 (b)
(
,
)
3.
3.32 (c)
,
3.34 (c)
(
,
)
4.
3.38
(
)
5.
3.324 (a),(b)
(
)
6.
3.44
(
)
7.
3.48
(
)
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_
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NOT from the textbook:
8.
Suppose a random variable
X
has the following probability density function:
≤
≤
=
otherwise
0
1
1
)
(
C
x
x
x
f
a)
What must the value of
C
be so that
f
(
x
)
is a probability density function?
b)
Find
P
(
X
< 2
)
.
c)
Find
P
(
X
< 3
)
.
d)
Find
μ
X
=
E
(
X
)
.
e)
Find
σ
X
2
=
Var
(
X
)
.
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9.
Let
X
be a continuous random variable
with the probability density function
f
(
x
)
=
k
⋅
x
2
,
0
≤
x
≤
1,
f
(
x
)
= 0,
otherwise.
a)
What must the value of
k
be so that
f
(
x
)
is a probability density function?
b)
Find the probability
P( 0.4
≤
X
≤
0.8 ).
c)
Find the median of the distribution of X.
d)
Find
μ
X
= E
(
X
).
e)
Find
σ
X
= SD
(
X
).
f)
Find the momentgenerating function of X, M
X
(
t
)
.
10.
Suppose a random variable
X
has the following probability density function:
≤
≤
⋅
=

otherwise
0
1
0
)
(
x
C
x
f
x
e
a)
What must the value of
C
be so that
f
(
x
)
is a probability density function?
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 Spring '08
 
 Normal Distribution, Probability theory, probability density function, insurance policy

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