Note:
There
will
be
no
detailed
solutions
provided
for these. We can discuss
solution generalities in class and during office hours. The test
and assignments (to be handed in) will be based in large part on
these
problem sets and the lectures.
Problem set #1 -to get you
going over the next month. This should
take us to Friday, Feb 11 although it may take a bit longer to cover
all the material. Start by going over some of the basic sigma field
questions, have a look at the convergence questions ( you may need to
review the sta347 material on these). Important points are that
intersections of sigma fields are sigma fields but not necessarily
unions, subsequences, Cauchy property of the various types of
convergence, open sets and the sigma fields generated by them, ...
l2 problems
This will help to give you a basic understanding of norms, metrics,
inner products,... We will cover this in lecture 2.
Problem set #2 - please try to
finish by the first lecture after reading week.
Problem set #3 - some problems
involving simple cts time processes, some more renewal problems, some
basic probability problems and inequalities.
Problem set #3ctd - some
further problems on cts time processes, martingales.
Problem set #4 - more problems
involving cts time ( a Gaussian process, birth process), martingales,
stopping times
The test covers all the above problem sets.