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Assignment #1, STAT331/361/SYDE334 Winter 2007
This assignment is to be handed in at the start of the lecture of
Thursday 18th January,
07
. For some problems required the application of R software, you need to cut and paste results
(either numeric or graphic) into Word, which can then edited, commented on and handed in. DO
NOT hand in R code, or a print out of the R session, unless asked for.
Problem 1
: Let
y
be the sample mean of observations
y
1
,...,y
n
.
(a) Show that
n
X
i
=1
(
y
i

y
)
2
=
n
X
i
=1
y
i
(
y
i

y
)
.
(b) Rewrite the above result in a matrix notation. For example, one may write
∑
n
i
=1
a
i
=
1
0
a
,
where
1
= (1
,...,
1)
0
is an
n
dimensional vector of all ones and
a
= (
a
1
,...,a
n
)
0
is the other
n
dimensional vector.
Problem 2
: Consider a normal random variable
X
∼
N
(2
,
4) or
X
∼
G
(2
,
2).
(a) Find mean E(
X
), variance var(
X
), and the second moment E(
X
2
).
(b) Show that
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 Winter '08
 YuliaGel

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