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Summary: Introduction to Generalized Linear Modelling,
Example Sheets 1, 2 and 3, with solutions
P.M.E.Altham, Statistical Laboratory, University of Cambridge.
May 26, 2008
These three Examples Sheets, and their solutions, have been built up from
1992, when I first gave this lecture course, to 2005, when I gave it for the
last time. I am grateful to many users, particularly undergraduates, for their
comments and questions. There is some overlap between these examples and
the examples in my lecture notes.
Example Sheet 1
(This is meant to be a very easy sheet, to get you started.)
1. Suppose X 1 , . . . , X n are i.i.d. Poisson random variables with parameter µ.
Show that “ µ = #X i /n, and var (“µ) = µ/n.
What is
E(- # 2 L
#µ 2
)?
What is the exact distribution of (n“µ)? What is the asymptotic distribution
of “
µ?
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