Statistics 2 (Edexcel AS and A level Modular Math)

1. Binomial Distribution

1.1. Factorial Notation and the Number of Arrangements

1.2. The Binomial Distribution

1.3. Conditions for a Binomial Distribution

1.4. Binomial Cumulative Distribution Function

1.5. Mean and Variance of a Binomial Distribution

1.6. Harder Problems

2. Poisson Distribution

2.1. Exponential Series and the Poisson Distribution

2.2. The Mean and Variance of a Poisson Distribution

2.3. The Poisson Cumulative Distribution Function

2.4. Conditions for a Poisson Distribution

2.5. The Poisson Approximation of a Binomial Distribution

2.6. Choosing a Binomial or Poisson Distribution

3. Continuous Random Variables

3.1. Continuous Random Variables and Their Probability Density Functions

3.2. The Cumulative Distribution Function

3.3. The Mean and Variance of a Probability Density Function

3.4. Finding the Mode, Median and Quartiles of a Continuous Random Variable

Revision Exercise 1

4. Continuous Uniform Distribution

4.1. Continuous Uniform/Rectangular Distribution

4.2. Properties of a Continuous Uniform Distribution

4.3. Choosing the Right Model

5. Normal Approximations

5.1. Continuity Correction

5.2. Approximating a Binomial Distribution by a Normal Distribution

5.3. Approximating a Poisson Distribution by a Normal Distribution

5.4. Choosing the Appropriate Approximation

6. Population and Samples

6.1. Populations, Censuses and Samples

6.2. The Advantages and Disadvantages of Taking a Census

6.3. Sampling

6.4. The Advantages and Disadvantages of Sampling

6.5. Simple Random Sampling

6.6. The Concept of a Statistic

6.7. The Sampling Distribution of a Statistic

7. Hypothesis Testing

7.1. The Concept of a Hypothesis Test

7.2. The Significance Level of a Hypothesis Test

7.3. One- and Two-Tailed Tests

7.4. Hypothesis Tests for the Proportion p of a Binomial Distribution and Hypothesis Tests for the Mean λ of a Poisson Distribution

7.5. Hypothesis Tests for the Proportion p of a Binomial Distribution and Hypothesis Tests for the Rate λ of a Poisson Distribution Using Critical Regions

Revision Exercise 2

Examination Practice Paper

Appendix

Answers

Index