STAT 443: Assignment 1
This assignment is to be handed in at the start of your lecture of
Friday 27th January
.
Please make sure that you write your name, student number and section number on your
script.
Some of these questions use R and so it is recommended that you work though the
tutorial at
http://www.stats.uwaterloo.ca/stats_navigation/StatSoftware/R/
You will need to cut and paste graphics from the R session into Word, which can then be
edited, commented on and handed in. Do not hand in R code, or a print out details of the
R session unless asked for.
Note that working with unfamiliar packages can take
much longer than you might have planned for, so do not leave this work to the
last minute.
1
Probability and Statistics Theory
1. Let
Z
t
be iid
N
(0
,
1) sequence and deﬁne
X
t
=
±
Z
t
t
even
Z
2
t

1

1
√
2
t
odd
.
(a) Compute
E
(
X
t
) for all
t
(b) Write down the moment generating function for
Z
t
and hence compute the ﬁrst
four noncentral moments of
Z
t
.
(c) Compute
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 Winter '09
 YuliaGel
 Forecasting, Normal Distribution, Variance, Probability distribution, Probability theory, probability density function, zt

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