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

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• Probabilidade e Estatística