Announcements:
(1) Here is Probability 34 assignment
for 2011. Note: the length of the assignment must be
equivalent more or less to the material of THREE lectures since it is
worth 20% of the mark. Please provide references for the external
material you have used.
(3) No specific lecture notes are provided for the course,
so if you've missed a lecture for some reason, please photocopy notes
from other students. Also here are some recommended sites, useful for
the course (mostly from
Wikipedia):
Q: Which proofs can be asked on the exam?
A: All of the course material is examinable (including the proof of the
strong law in the harder case).
Q: Suppose Xn are independent, and Xn→X in
probability. How to show that X
is a.s. a constant?
A: Suppose that X is not
a constant a.s. What does this mean? Can there
be α and β with α<β, such that
P(X<α)>0 and P(X>β)>0 ? Now use
independence of Xn
and Xn+1.
Q: Which proofs can be asked on the exam?
A: All of the course material is examinable (including the proof of the
strong law in the harder case).
Q: If asked to prove that convergence a.s. implies convergence in
probability, would we need to state and prove the Lemma (Xn→X a.s. iff
P(sup|Xn-X|>epsilon)→0 ) as stated in the notes?
A: Yes, as it is essentially the proof of the statement.