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Statistics
NYU  Spring 2012
Prof. Giuseppe Arbia
V31.0018  006
1
st
homework
Thursday January, 26
th
2012
Answer each of the questions. Read the questions carefully and keep your answers brief and to the
point. PLEASE WRITE NEATLY.
Please leave your homework in the mailbox of your respective Teaching Assistant by Monday at
1:30. Since the homework will be discussed during the Lab sessions, no late homework can be
accepted. Good work !
Question 1
: It is given the variable X assuming the values {1, 4, 6, 2, 8, 4, 9, 7, 5}
a) What is the value of x
3
?
b) and the value of
n
?
c) and the mean of X?
d) Calculate the following expressions:
a)
x
i
i
=
1
5
"
b)
x
i
2
i
=
1
5
"
c)
x
i
i
=
2
4
"
d)
(
)
∑
=
5
3
2
i
i
i
x
Question 2:
For any given sequence
x
1
,
x
2
,...,
x
n
{
}
and for any constant terms
a
and
b,
demonstrate that:
a)
(
ax
i
i
=
1
n
"
+
by
i
)
=
a
x
i
i
=
1
n
"
+
b
y
i
i
=
1
n
"
b)
(
ax
i
+
b
)
i
=
1
n
"
=
a
x
i
i
=
1
n
"
+
nb
Solve the expression:
c)
(
ax
i
+
b
)
2
i
=
1
n
"
Question 3:
a)
What is the value of an observation such that, added to our database, the mean does not change ?
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 Spring '12
 GiuseppeArbia
 Statistics, i=1, Prof. Giuseppe Arbia

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