Math 301

P&SI

Dr. McLoughlin

11
Fall of 2011
11 Handout 3 2011 2012
Random Variables: Continuous
Dr. M. P. M. M. McLoughlin
Revised 2011
Note: The basic building block of probability is set theory: Suppose we have a well dened
sample space S and eve
MATH 301 P & S I FALL 2009 WORKSHEET IIIAA
NAME:_
Revised Fall 2011
6.1. Claim: Let
(please print legibly)
S and S be a well defined sample space with A B events with Pr(A  B) > and
Pr(B) 0. Therefore it is the case that Pr(B  A) < . Prove or disprove t
Math 301

P&SI

Dr. McLoughlin

7
Fall of 2011
7 Worksheet 3D 2011 2012
Exercises about Conditional Probability
Dr. M. P. M. M. McLoughlin
Revised 2011
Prove or disprove the following claims:
Claim 7.1. Let U be a well dened universe and S be a well de
MATH 301 P & S I FALL 2006 WORKSHEET IIIC NAME:_
(please print legibly)
1.
Let the sample space S = U be well defined and let R, S, and T be events. With the probabilities assigned
for events as given in the Venn Diagramme determine if R, S, and T are ind
Math 301 P & S I Fall 2008
Worksheet IV
Name:_
(please print legibly)
Show all work. If an answer DNE, explain why it does not exist.
1. Consider the following probability mass function (pmf) :
X=x
Pr(X = x)
2
0.05
1
0.11
0
0.56
1
0.18
2
0
3
0.1
Graph the
Math 301

P&SI

Dr. McLoughlin

3
Spring of 2013
3AAAAA Worksheet
Probability & Combinatorics
Dr. M. P. M. M. McLoughlin
Revised 2013
page 44 in Ghahramani text. 3, 7, 9.
page 63 in Ghahramani text. 1, 3, 7.
page 71 in Ghahramani text. 13.
1. There is
MATH 301 P & S I FALL 2008 WORKSHEET III NAME:_
(please print legibly)
1. Suppose S be a well defined sample space with A
B events and we know that Pr (A) = 0.75, Pr(B) = 0.48; and,
Pr(A B) = 0.89.
A. Find Pr(A  B)
C
E. Find Pr(A  B)
B. Find Pr(B  A)
MATH 301 P & S I FALL 2009 WORKSHEET IIIB
NAME:_
(please print legibly)
1. There is an urn. It contains 5 white, 3 red, and 6 blue balls.
A ball is drawn then another.
Find the probability that of the balls the second is white given the first is red.
2. T
Math 301

P&SI

Dr. McLoughlin

8
Fall of 2011
8 Worksheet 3E 2011 2012
Exercises about Conditional Probability
Dr. M. P. M. M. McLoughlin
Revised 2011
Jablonskis Principle from Set Theory. Let U be a well dened universe and let A and B be
sets. It is
Math 301

P&SI

Dr. McLoughlin

1
Fall of 2011
1 Worksheet 2011 1B
On the Na or Intuitive Idea of Probability
ve
Computational  Not For Required Board Credit
Dr. M. P. M. M. McLoughlin
Revised 2011
This is an exercise set that incorporates both your i
Math 301

P&SI

Dr. McLoughlin

1
Fall of 2011
1 Worksheet 2011 2
The Axioms of Probability Theory, Set Theory, and Real Variables
Dr. M. P. M. M. McLoughlin
Revised 2011
Mathematics is predicated on logic (for the rules of inference) and on Set Theory
Math 301  Probability & Statistics I Dr. McLoughlin  Worksheet 0 version 2 Fall 2011
Worksheet Zero
Foundations and Calculus
Prerequisite Concepts
Dr. M. P. M. M. McLoughlin
Fall 2011
Prove means to rigorously prove a claim is so from the premises of
Math 301 Probability and Statistics  Dr. McLoughlins Class The Gamma Function page 1 of 5
MATH 301 PROBABILITY AND STATISTICS
DR. MCLOUGHLINS CLASS
THE GAMMA FUNCTION
HANDOUT 4
We will look a little more closely at the Gamma Function. Source for this dis
Math 301  P & S I  Dr. McLoughlin  Handout
Spring of 2009
1
14
Handout
The Lemmas We Need for Basic Proofs
Dr. M. P. M. M. McLoughlin
Spring 2009
Add to our Axiom handout in between corollary 3 and theorem 1:
Corollary 4: Let S be a well dened sample s
Math 301

P&SI

Dr. McLoughlin 
1
Spring of 2013
1 Handout 1 of 2013
The Axioms of Probability Theory,
With Set Theory and Real Variables, too.
Dr. M. P. M. M. McLoughlin
Revised 2013
Mathematics is predicated on logic (for the rules of inference) and
Math 301

P&SI

Dr. McLoughlin

9
Fall of 2011
9 Handout 2 2011 2012
Random Variables: Discrete
Dr. M. P. M. M. McLoughlin
Revised 2011
Note: The basic building block of probability is set theory: Suppose we have a well dened
sample space S and events
Math 301

P&SI

Dr. McLoughlin

1
Fall of 2011
1 Worksheet 0 Problem 16
Rigourously Done (As on the Board, a Quiz, or a Test)
Dr. M. P. M. M. McLoughlin
Revised 2011
16. (Math 224) Prove or disprove the following claim.
h : N R h(x) = 3 x + 5.
A. Claim
Math 301

P&SI

Dr. McLoughlin

1
Spring of 2013
1 Worksheet 2011 1A
On the Na or Intuitive Idea of Probability
ve
Computational  Not For Required Board Credit
Dr. M. P. M. M. McLoughlin
Revised 2013
This is an exercise set that incorporates both your
Math 301

P&SI

Dr. McLoughlin

5
Fall of 2011
5 Worksheet 2011 2012
Claims about Probability and Conditional Probability
Dr. M. P. M. M. McLoughlin
Revised 2011
1. Section 1
Was material from worksheet 0
2. Section 2
Was material from worksheet 1
3. S
1
Math 301  P & S I  Dr. McLoughlin  Worksheet 4 2
10
Fall of 2011
Worksheet 4 1
2
10 Basic Claims for Discrete Random Variables
Dr. M. P. M. M. McLoughlin
Starred claims are (in my opinion) quite challenging and as such I do not expect us to successfu