Probability, Statistics and Sets

1. Introduction to Sets 1

• Definition of Set Theory
• Representing Sets
• Empty Set
• Set Symbols
• The Sets of Natural Numbers and Whole Numbers
• The Cardinal Numbers of a set
• Equal and Equivalent Sets
• Finite and Infinite Sets

2. Introduction to Sets 2

• Subsets
• Proper Sets
• Counting Subsets and Proper Sets

3. Set Operations and Venn Diagram

• Universal Sets
• Venn Diagram
• The Complement Operation
• The Union Operation
• The Intersection Operation
• The Difference Operation
• Multiple Operation on Two Sets
• Multiple Operation on Three Sets
• Cardinal Number Formula
• AND / OR Operations

4. De Morgan’s Law and Set Equality

• De Morgan’ Law for Sets
• Equality with Three Sets
• Shading Venn Diagrams

5. Survey Problems and Set Applications

• Survey Problems with Two Sets
• Survey Problems with Three Sets

6. Introduction to Basic Logics

• Statements
• Types of Statements
• Negation of Statements
• Negation of Universal and Particular Statements

7. Conjunctions, Disjunctions and Truth Table

• Definition of Conjunction and Disjunction
• The Negation of Truth Table
• Building of Truth Table of Two Variable
• Building of Truth Table of Three Variable

8. Logical Equivalence and De Morgan’s Law For Logics

• Logical Equivalence
• De Morgan’s Law for Logics
• De Morgan’s Law and Quantifiers

9. Conditional Statements and Implications

• The Conditional Statements
• Other Forms of Conditional Statements
• The Negation of Conditional Statements
• The Family of Conditional Statements
• The Biconditional Statements
• Contradictions, Tautologies and Implications

10. Analyzing Arguments

• Valid or Invalid Arguments
• Symbolic Arguments
• Tautologies Revisited
• Determining a Logical Conclusion

11. Syllogistic Arguments

o        Valid or Invalid Arguments

o        Definition of Symbolic Arguments

o        Euler Diagrams

Contents of Probability

1. Organized Counting

• Combinatorics
• Combinatoric Terminology
• One Part Task
• Counting by Observation
• Making a List
• Two Part Task
• Counting by Making a Product Table
• Two Fair Dice
• Three Part Task
• Tree Diagram for Three Coins
• Multi Part Task
• Counting Outcomes at the Ballgame

2. Permutations

• Definition of Permutation
• Product Formula for Permutation
• (Fundamental Counting Principle)
• Factorial Permutation Formula
• Guidelines for Using Permutations
• Permutations of Non-distinct Objects

3. Combinations

o Definition of Combination

o Quotient Formula for Combinations

o Factorial Formula for Combinations

o Guideline for Choosing a Method

4. Fundamentals of Probability

o Introductory Terminology

o Empirical Probability

o Theoretical Probability

o Probability Distribution Tables

o The Complement Principle of Probability

5. Multiplication and Addition of Probability

• Independent and Dependent Events of Probability
• Multiplication Formula for Independent Events
• Probability with Replacement
• Probability without Replacement
• Addition Formula of Probability and Mutually Exclusive of Probability
• Combined Multiplication and Addition Probability

6. Conditional Probability

• Definition of Conditional Probability
• Relationship between Multiplication and Conditional Probability

o        Dependent Probability

o        Independent Probability

7. Bayes’ Theorem

• Bayes’ Elimination Rule
• Bayes’ Theorem

8. Binomial Probability (Success and Failure)

• Definition of Binomial Probability and it’s Formula
• Binomial Probability with Multiple Success

9. Probability Distribution Table

• Constructing Probability Distribution Tables by Using Binomial Probability

10. Odds in Favor and Odds Against

• Odds in Favor
• Odds against
• Odds as the Ratio of Outcomes
• Determining Probabilities from Odds

11. . Expected Value
    • Definition of Expected Value and it’s Formula
    • The Game is not Fair ( Fair Game )

Contents of Statistics

12. Introduction to Statistics

• Definition of Statistics
• Statistical Terminology

13. Descriptive and Inferential Statistics

• The Difference between Descriptive and Inferential Statistic
• The Difference between Population and Sample
• The Difference between Parameter and Statistic

14. Frequency Distribution

• Definition of Frequency Distribution
• Table of Frequency Distribution
• Relative Frequency Distribution
• Cumulative Frequency Distribution

15. Statistical Charts and Graphs

• Pie Charts
• Bar Graphs
• Pareto Charts

16. Histograms

• Constructing Histograms

17. Stem and Leaf Plots

• Plotting Stem and Leaf Diagrams

18. The Mean

• Definition of Mean and it’s Formula
• Calculating the Mean from Frequency Distribution Table
• Calculating the Mean of Class Intervals
• Calculating the Weighted Mean for academic Purposes

19. The Median and Mode

• Definition of Median and it’s Formula
• Definition of Mode and it’s Formula
• Calculating the Median from Frequency Distribution Table
• Calculating the Mode from Frequency Distribution Table

20. Measures of Data Location

• Percentiles and their Calculation
• Calculating Percentiles from Stem and Leaf Plots
• Deciles and their Calculation
• Quartiles and their Calculation
• Box and Whisker Plot and Five Number Summary
• Calculating the InterQuartile Range ( IQR )
• The Effects of Outliers

21. Measures of Dispersion

• Definition of Dispersion and Spread
• The Range of a Data
• Population Variance and Population Standard Deviation
• Definition Formula and Computational Formula
• Sample Variance and Sample Standard Deviation

22. Sampling Distribution

• Definition of Sampling Distribution
• Types of Distributions

o        Normal Distribution

o        Skewed Distribution

o        Uniform Distribution

23. Central Limit Theorem

• Definition of Central Limit Theorem
• Z-Score and Z-Table
• Word Problem Solving

24. Population Proportions

• Definition of Population Proportion
• Central Limit Theorem for Population Proportion
• Word Problem Solving

25. Confidence Intervals

• Confidence Interval for Population Proportion
• Finding the Sample Size, Given the Margin of Error.

26. Chi-Square Distribution

• Definition of Chi-Square Distribution
• Definition of Chi-Square Table

27. Estimating Population Variance and

       Population Standard Deviation

• The Procedure for Finding Confidence Interval of

Population Variance and Standard Deviation

28. Introduction to Hypothesis Testing

• Definition of Hypothesis

o        Null Hypothesis

o        Alternative ( Research ) Hypothesis

• Steps for Hypothesis Testing

o        Identifying Hypothesis

o        Finding Test-Statistic

o        Making Decisions and Conclusions

29. Hypothesis Testing for Population Means

• Steps for Finding Hypothesis Testing for means
• Word Problem Solving and Examples

30. Hypothesis Testing for Population Parameter

• Steps for Finding Hypothesis Testing for Population Parameter
• Word Problem Solving and Examples

31. P-value for Hypothesis Tasting

• Definition for Hypothesis Testing
• Difference between P-value Method and Traditional Method
• Steps for P-value Method
• Hypothesis Testing for Means Using P-value Method
• Hypothesis Testing for Population Parameter Using P-value Method

32. Hypothesis Testing for Population Variance

          and Population Standard Deviation

• Definition of Hypothesis Testing for Population Variance and Population Standard Deviation
• Steps of Hypothesis Testing for Population Variance and Population Standard Deviation
• Word Problem Solving and Examples

33. Hypothesis Testing for Two Means

          (Large Independent Samples)

• Definition of Hypothesis Testing for Two Means
• Steps of Hypothesis Testing for Two Means
• Word Problem Solving and Examples

34. Hypothesis Testing for Two Means

          (Small Independent Samples)

• Definition of Hypothesis Testing for Two Means
• Steps of Hypothesis Testing for Two Means
• Word Problem Solving and Examples