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Statistics 5101, Fall 2010: Homework
Assignment 2
1. Suppose
X
is a random variable having the discrete uniform distribution
on the sample space
{
1
,
2
,
3
,
4
,
5
,
6
}
.
(a) Determine Pr(
X <
4).
(b) Determine Pr(
X
≤
4).
(c) Determine Pr(6
< X <
10).
2. Suppose
X
is a random variable having PMF
f
(
x
) =
x
21
,
x
= 1
,
2
,
3
,
4
,
5
,
6
.
(d) Determine
E
(
X
).
(e) Determine
E
(
X
2
).
(f) Determine
E
{
(
X

3)
2
}
.
3. Suppose
X
is a Ber(
p
) random variable.
(g) Show that
E
(
X
k
) =
p
for all positive integers
k
.
(h) Determine
E
{
(
X

p
)
2
}
.
(i) Determine
E
{
(
X

p
)
3
}
.
4. Determine the set of real numbers
θ
such that
f
θ
(
x
) =
θ,
x
=
x
1
θ
2
,
x
=
x
2
1

θ

θ
2
, x
=
x
3
is a PMF on the sample space
{
x
1
,x
2
,x
3
}
.
5. Suppose we have a PMF
f
with domain
S
(the original sample space), and
we have a map
g
:
S
→
Ω that induces a probability model with PMF pr
with domain Ω (the new sample space) given by the formula on slide 107.
Prove that for any realvalued function
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This note was uploaded on 12/01/2010 for the course STAT 5101 taught by Professor Staff during the Fall '02 term at Minnesota.
 Fall '02
 Staff
 Statistics

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