02/08/2017
Preliminaries: Probability
Definition 1: A sample space S is the set of all possible outcomes for an experiment.
Equiprobable all the outcomes are equally likely, i.e., a fair experime
02/06/2017
Theorem 1. Let p, q, and r be statements. Then, we have the following equivalences:
p p
p p p p p
p q q ~p
p q q p
p q q p
p q q p
p q r p q r
p q r p
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02/15/2017
Conditional Probabilities
Example. X and Y are two events such that P X|Y 0.4, P Y 0.25, and P X 0.2.
Find:
a
b
c
P Y|X
P XY
P XY
Solution.
b
c
P XY P X|Y P Y 0.4
02/20/2017
Independent Events (Revisited)
Let A, B independent events, Then
P A|B
P AB
PB
PAPB
PB
PA
Similarly, P B|A P B .
Note: P AB P A|B P B P A P B .
Tests for Independence
T
ALABAMA A & M UNIVERSITY, COLLEGE OF ENGINEERING,
TECHNOLOGY, & PHYSICAL SCIENCES
Mathematics 500
Quiz #1
Due Date: February 15 (in class)
Instructor: Dr. Ncube
Full Name:
Student Number:
1. In your o
ALABAMA A & M UNIVERSITY, COLLEGE OF
ENGINEERING,
TECHNOLOGY, & PHYSICAL SCIENCES
Mathematics 500
Full
Name:
Jessica Burton
Student
Number
1.
2.
Quiz #1
Due Date: February 15 (in
class)
Instructor: Dr
ALABAMA A & M UNIVERSITY, COLLEGE OF ENGINEERING,
TECHNOLOGY, & PHYSICAL SCIENCES
Mathematics 500
Quiz #2
February 15 (in class)
Instructor: Dr. Ncube
Full Name:
Student Number:
Consider the sets A =