Probability & Statistics

UNIT 1: Introduction to Statistics

1.1 Introduction
1.2 Data Collection and Descriptive Statistics
1.3 Inferential Statistics and Probability Models
1.4 Populations and Samples
1.5 A Brief History of Statistics

UNIT 2: Descriptive Statistics

2.1 Introduction
2.2 Describing Data Sets
2.3. Frequency Tables and Graphs
2.4 Relative Frequency Tables and Graphs
2.5 Grouped Data, Histograms, Ogives, and Stem and Leaf Plots
2.6 Summarizing Data Sets
2.7 Sample Mean, Sample Median, and Sample Mode
2.8 Sample Variance and Sample Standard Deviation
2.9 Sample Percentiles and Box Plots
2.10 Chebyshev’s Inequality
2.11 Normal Data Sets
2.12 Paired Data Sets and the Sample Correlation Coefficient

UNIT 3: Elements of Probability

UNIT 4: Random Variables and Expectation

4.1 Random Variables
4.2 Types of Random Variables
4.3 Jointly Distributed Random Variables
4.4 Independent Random Variables
4.5 Conditional Distributions.
4.6 Expectation.
4.7 Properties of the Expected Value
4.8 Expected Value of Sums of Random Variables
4.9 Variance
4.10 Covariance and Variance of Sums of Random Variables
4.11 Moment Generating Functions
4.12 Chebyshev’s Inequality and the Weak Law of Large Numbers

UNIT 5: Special Random Variables

5.1 The Bernoulli and Binomial Random Variables
5.2 Computing the Binomial Distribution Function
5.3 The Poisson Random Variable
5.4 Computing the Poisson Distribution Function.
5.5 The Hypergeometric Random Variable.
5.6 The Uniform Random Variable.
5.7 Normal Random Variables
5.8 Exponential Random Variables
5.9 The Poisson Process
5.10 The Gamma Distribution
5.11 Distributions Arising from the Normal.
5.12 The Chi-Square Distribution.
5.13 The t-Distribution
5.14 The F-Distribution
5.15 The Logistics Distribution

UNIT 6: Distributions of Sampling Statistics

6.1 Introduction
6.2 The Sample Mean
6.3 The Central Limit Theorem
6.4 Approximate Distribution of the Sample Mean
6.5 How Large a Sample Is Needed?
6.6 The Sample Variance
6.7 Sampling Distributions from a Normal Population
6.8 Distribution of the Sample Mean
6.9 Joint Distribution of X and S²
6.10 Sampling from a Finite Population

UNIT 7: Parameter Estimation

7.1 Introduction
7.2 Maximum Likelihood Estimators
7.3 Estimating Life Distributions
7.4 Interval Estimates
7.5 Confidence Interval for a Normal Mean When the Variance Is Unknown
7.6 Confidence Intervals for the Variance of a Normal Distribution
7.7 Estimating the Difference in Means of Two Normal Populations
7.8 Approximate Confidence Interval for the Mean of a Bernoulli Random Variable
7.9 Confidence Interval of the Mean of the Exponential Distribution
7.10 Evaluating a Point Estimator
7.11 The Bayes Estimator

UNIT 8: Hypothesis Testing

8.1 Introduction
8.2 Significance Levels
8.3 Tests Concerning the Mean of a Normal Population
8.4 Case of Known Variance
8.5 Case of Unknown Variance: The t-Test
8.6 Testing the Equality of Means of Two Normal Populations
8.7 Case of Known Variances
8.8 Case of Unknown Variances
8.9 Case of Unknown and Unequal Variances
8.10 The Paired t-Test
8.11 Hypothesis Tests Concerning the Variance of a Normal Population
8.12 Testing for the Equality of Variances of Two Normal Populations
8.13 Hypothesis Tests in Bernoulli Populations
8.14 Testing the Equality of Parameters in Two Bernoulli Populations
8.15 Tests Concerning the Mean of a Poisson Distribution
8.16 Testing the Relationship Between Two Poisson Parameters

UNIT 9: Regression

9.1 Introduction
9.2 Least Squares Estimators of the Regression Parameters
9.3 Distribution of the Estimators.
9.4 Statistical Inferences About the Regression Parameters.
9.5 Inferences Concerning B
9.6 Inferences Concerning a
9.7 Inferences Concerning the Mean Response α + ẞxo
9.8 Prediction Interval of a Future Response
9.9 Summary of Distributional Results
9.10 The Coefficient of Determination and the Sample Correlation Coefficient
9.11 Analysis of Residuals: Assessing the Model
9.12 Transforming to Linearity
9.13Weighted Least Squares
9.14 Polynomial Regression
9.15 Multiple Linear Regression
9.16 Predicting Future Responses
9.17 Logistic Regression Models for Binary Output Data

IGCSE

Primary Year

Secondary Year

Junior College

Poly Technique

Course Content

UNIT 1: Introduction to Statistics

1.1 Introduction

1.2 Data Collection and Descriptive Statistics

1.3 Inferential Statistics and Probability Models

1.4 Populations and Samples

1.5 A Brief History of Statistics

UNIT 2: Descriptive Statistics

2.1 Introduction

2.2 Describing Data Sets

2.3. Frequency Tables and Graphs

2.4 Relative Frequency Tables and Graphs

2.5 Grouped Data, Histograms, Ogives, and Stem and Leaf Plots

2.6 Summarizing Data Sets

2.7 Sample Mean, Sample Median, and Sample Mode

2.8 Sample Variance and Sample Standard Deviation

2.9 Sample Percentiles and Box Plots

2.10 Chebyshev’s Inequality

2.11 Normal Data Sets

2.12 Paired Data Sets and the Sample Correlation Coefficient

UNIT 3: Elements of Probability

3.1 Introduction

3.2 Sample Space and Events

3.3 Venn Diagrams and the Algebra of Events

3.4 Axioms of Probability

3.4 Axioms of Probability

3.6 Conditional Probability

3.7 Bayes’ Formula

3.8 Independent Events

UNIT 4: Random Variables and Expectation

4.1 Random Variables

4.2 Types of Random Variables

4.3 Jointly Distributed Random Variables

4.4 Independent Random Variables

4.5 Conditional Distributions.

4.6 Expectation.

4.7 Properties of the Expected Value

4.8 Expected Value of Sums of Random Variables

4.9 Variance

4.10 Covariance and Variance of Sums of Random Variables

4.11 Moment Generating Functions

4.12 Chebyshev’s Inequality and the Weak Law of Large Numbers

UNIT 5: Special Random Variables

5.1 The Bernoulli and Binomial Random Variables

5.2 Computing the Binomial Distribution Function

5.3 The Poisson Random Variable

5.4 Computing the Poisson Distribution Function.

5.5 The Hypergeometric Random Variable.

5.6 The Uniform Random Variable.

5.7 Normal Random Variables

5.8 Exponential Random Variables

5.9 The Poisson Process

5.10 The Gamma Distribution

5.11 Distributions Arising from the Normal.

5.12 The Chi-Square Distribution.

5.13 The t-Distribution

5.14 The F-Distribution

5.15 The Logistics Distribution

UNIT 6: Distributions of Sampling Statistics

6.1 Introduction

6.2 The Sample Mean

6.3 The Central Limit Theorem

6.4 Approximate Distribution of the Sample Mean

6.5 How Large a Sample Is Needed?

6.6 The Sample Variance

6.7 Sampling Distributions from a Normal Population

6.8 Distribution of the Sample Mean

6.9 Joint Distribution of X and S²

6.10 Sampling from a Finite Population

UNIT 7: Parameter Estimation

7.1 Introduction

7.2 Maximum Likelihood Estimators

7.3 Estimating Life Distributions

7.4 Interval Estimates