ELEMENTARY PROBABILITY THEORY

• Instructor: Lagos City Polytechnic
• Lectures: 8
• Duration: 10 weeks

COURSE OUTLINE

SETS & SUBSETS

Sets

Notation

Finite and Infinite sets

Equality of sets

Null Set

Subsets

Proper subsets

Comparability

Set of sets

Universal set

Power set

Disjoint sets

Venn-Euler diagrams

Axiomatic development of set theory

Conclusion

Summary

Tutor-Marked assignment

References and Further readings

BASIC SET OPERATION

                        Union

Intersection

Difference

Complement

Operations on Comparable Sets

FUNCTIONS

Definition

Mappings, Operators, Transformations

Equal functions

Range of a function

One – One functions

Onto functions

Identity function

Constant Functions

Product Function

Associativity of Products of Functions

Inverse of a function

Inverse Function

Theorems on the Inverse Function

Ordered Pairs

Product Set

Coordinate Diagrams

Graph of a Function

Properties of the graph of a function

Graphs and Coordinate diagrams

Properties   of   Graphs   of   Functions   on   Coordinate diagrams

Functions as sets of ordered pairs

Product Sets in General

RELATIONS

Propositional Functions, Open Sentences

Relations

Solution Sets and Graphs of relations

Relations as Sets of Ordered Pairs

Reflexive Relations

Symmetric Relations

Anti-Symmetric Relations

Transitive Relations

Equivalence Relations

Domain and Range of a Relation

Relations and Functions

MATHEMATICS OF COUNTING

Fundermental principle of counting

The relative frequency approach

The classical approach

Permutation of n distinct objects

Permutation of Indistinguishable Objects

Combination

Partitioning

ELEMENTARY PRINCIPLE OF THE THEORY OF PROBABILITY

Properties of probability

Conditional probability

Bayes Theorem