lecture:
problem set These problems relate to
material not found in the text.
relevent text sections:
the
indicator
r.v.
is
on
p37,
1.3,
1.5, 4.1, 4.2
suggested problems from
the text: Section 1.8: 47, 49, 51, 53, 57, 59, 61, 64 (show that
conditional P satisfies the Kolmogorov Axioms),
lecture#3
lecture:
problem set: Section
2.5: 1, 3, 11, 13, 15, 17, 21, 23, 27, 29. Section 4.7: 2, 3, 7, 15,
27, 30, 35, 83 (use pgf's), 85 (you may also use pgf's), 94
relevent text
sections: 2.1, 4.1, 3.4, 4.1, 4.2, 4.5
lecture#4
lecture:
problem set: Section
2.5: 5, 6, 7, 19, 33, 35, 40, 41. Section 4.7: 5, 8 (challenge), 13
(challenge), 31, 33 ( special case of Chebyshev), 42, 49, 50, 55, 57,
71 (application of conditioning in the discrete case), 79, 81, 85 (use
mgf's), 95, 97.
relevent text sections:
2.1, 2.2(up to p52, 4.1, 4.2, 4.5, cumulative distribution
function for both the discrete and cts cases (pp 36, 48), p121
(Markov),
pp 133, 134 (Chebyshev), p174 (pgf),
lecture#5
lecture:
problem set: Section
2.5: 39, 40, 41
relevent text sections:
pp35-37, pp47-52,
Lecture#6 (test!)
Test Date: Wed, Oct 16
from
7-10PM
and
Test Location:
SS2110 and the lecture room. Please see the announcement on Blackboard
for your room.
Note: The test covers
the first 5 lectures as done in class and on the web. Please do
the
pratice test.
lecture#7
lecture:
problem set: Section
4.7: 7, 13 (do in a rigorous way using integration by parts), 14, 16,
21, 23, 25, 31, 35, 43 {Note: cov(X,Y)=E(XY)-E(X)E(Y)}, 50, 55, 57, 79,
81, 83, 85, 89, 91, p189 #9 ( note that a binomial is a sum of
Bernoulli rv's and so the CLT may apply, see #8 on that page for the
Poisson)
relevent text sections:
2.2.1, 2.2.2, 2.2.3, 2.3, 4.1.2, 4.2, 4.5, p184
lecture#8
lecture:
problem set: Section 2.5: 45, 47, 50, 51, 53, 55, 57, 59, 60,
61, 62, 63, 65, 67, 69, 71 Section 3.8: 1, 3, 7, 9, 11, 15, 17, 19, 25,
42(a), 43, 47, 51, 55 Section 6.4: 3, 5, 7
Note: For some of the
problems you will need the notion of a conditional pf or pdf. This is
f(y|x)=f(x,y)/f(x), where f(x,y) is the joint pf/pdf and f(x) is the
"marginal" pf/pdf of the first component. You need only calculate these
for now. Conditioning in the cts case is tricky. In the discrete case
it is basically conditional probability.
relevent text sections:
2.2.4, 2.3, Chapter 3 ( omit sections 3.5 and 3.7 for now) Note: 3.6.2
deals with the change of variables formula (see also p62), Chapter 6
(omit 6.3 for now)
lecture#9
lecture: This is a fairly long lecture.
Please note the definition of correlation on the last page. You will
need to read about the bivariate normal and the Student-t distribution.
problem set:
Section 2.5: 39, 48, 56 Section 3.8: 6, 8, 13, 23, 33, 49, 52, 57, 59,
61, 63, 65 Section 4.7: 25, 43, 47, 53, 57, 59, 63, 71, 73, 77, 79, 95
Section 6.4: 5, 6, 7
Challenge problem: Derive the
pdf of a Student-t rv with n degrees of freedom using its relationship
to the F distribution.
relevent text sections:
3.5, 3.6, 4.3, 2.2.4, 6.2
lecture#10
lecture:
problem set: Section
3.8: 13, 22, 23, 45, 64, 70 Section 4.7: 5, 7, 9, 33, 45, 49, 68,
69, 75, 93 Section 6.4: 3, 8
relevent text sections:
3.2 (for the multinomial), 3.5, 4.3, 4.4,
lecture#11
lecture:
problem set: Section
3.8: 69, 71, 73, 75, 77, 78, 79, 81 Section 4.7: 17, 19, 61 Section
5.4: 1, 3, 5, 7, 9, 15, 17, 29
relevent text sections:
Chapter 3.7, 5, 6.3
lecture#12
Coverage of any missed topics. Review of the course and discussion
related to the exam.