Complete Probability & Statistics 2 for Cambridge International AS & A Level

Syllabus matching grid
1 The Poisson distribution
1.1: Introducing the Poisson distribution
1.2: The role of the parameter of the Poisson distribution
1.3: The recurrence relation for the Poisson distribution
1.4: Mean and variance of the Poisson distribution
1.5: Modelling with the Poisson distribution
2 Approximations involving the Poisson distribution
2.1: Poisson as an approximation to the Binomial
2.2: The Normal approximation to the Poisson distribution
3 Linear combination of random variables
3.1: Expectation and variance of a linear function of a random variable
3.2: Linear combination of two (or more) independent random variables
3.3: Expectation and variance of a sum of repeated independent observations of a random variable, and the mean of those observations
3.4: Comparing the sum of repeated independent observations with the multiple of a single observation
Review exercise A
Maths in real-life: The mathematics of the past
4 Linear combination of Poisson and Normal variables
4.1: The distribution of the sum of two independent Poisson random variables
4.2: Linear functions and combinations of normal random variables
5 Continuous random variables
5.1: Introduction to continuous random variables
5.2: Probability density functions
5.3: Mean and variance of a continuous random variable
5.4: Mode of a continuous random variable
6 Sampling
6.1: Populations, census and sampling
6.2: Advantages and disadvantages of sampling
6.3: Variability between samples and use of random numbers
6.4: The sampling distribution of a statistic
6.5: Sampling distribution of the mean of repeated observations of a random variable
6.6: Sampling distribution of the mean of a sample from a normal distribution
6.7: The Central Limit Theorem
6.8: Descriptions of some sampling methods
Review exercise B
Maths in real-life: Modelling statistics
7 Estimation
7.1: Interval estimation
7.2: Unbiased estimate of the population mean
7.3: Unbiased estimate of the population variance
7.4: Confidence intervals for the mean of a Normal distribution
7.5: Confidence intervals for the mean of a large sample from any distribution
7.6: Confidence intervals for a proportion
8 Hypothesis testing for discrete distributions
8.1: The logical basis for hypothesis testing
8.2: Critical region
8.3: Type I and Type II errors
8.4: Hypothesis test for the proportion p of a Binomial distribution
8.5: Hypothesis test for the mean of a Poisson distribution
9 Hypothesis testing using the Normal distribution
9.1: Hypothesis test for the mean of a Normal distribution
9.2: Hypothesis test for the mean using a large sample
9.3: Using a confidence interval to carry out a hypothesis test
Review exercise C
Maths in real-life: A risky business
List of formulae
Answers
Glossary of terms
Index