Further statistics 1

1. DISCRETE RANDOM VARIABLES

1.1 Expected value of a discrete random variable

1.2 Variance of a discrete random variable

1.3 Expected value and variance of a function of $X$

1.4 Solving problems involving random variables

1.5 Mixed exercise 1

1.6 Review exercise for chapter 1

 

2. POISSON DISTRIBUTIONS

2.1 The Poisson distribution

2.2 Modelling with the Poisson distribution

2.3 Adding Poisson distributions

2.4 Mean and variance of a Poisson distribution

2.5 Mean and variance of the binomial distribution

2.6 Using the Poisson distribution to approximate the binomial distribution

2.7 Mixed exercise 2

2.8 Review exercise for chapter 2

 

3. GEOMETRIC AND NEGATIVE BINOMIAL DISTRIBUTIONS

3.1 The geometric distribution

3.2 Mean and variance of a geometric distribution

3.3 The negative binomial distribution

3.4 Mean and variance of the negative binomial distribution

3.5 Mixed exercise 3

3.6 Review exercise for chapter 3

 

4. HYPOTHESIS TESTING

4.1 Testing for the mean of a Poisson distribution

4.2 Finding critical regions for a Poisson distribution

4.3 Hypothesis testing for the parameter p of a geometric distribution

4.4 Finding critical regions for a geometric distribution

4.4 Mixed exercise 4

4.5 Review exercise for chapter 4

 

5. CENTRAL LIMIT THEOREM

5.1 The central limit theorem

5.2 Applying the central limit theorem to other distributions

5.3 Mixed exercise 5

5.4 Review exercise for chapter 5

 

6. CHI-SQUARED TESTS

6.1 Goodness of fit

6.2 Degrees of freedom and the chi-squared family of distributions

6.3 Testing a hypothesis

6.4 Testing the goodness of fit with discrete data

6.5 Using contingency tables

6.6 Applying goodness-of-fit tests to geometric distributions

6.7 Mixed exercise 6

6.8 Review exercise for chapter 6

 

7. PROBABILITY GENERATING FUNCTIONS

7.1 Probability generating functions

7.2 Probability generating functions of standard distributions

7.3 Mean and variance of a distribution

7.4 Sums of independent random variables

7.5 Mixed exercise 7

7.6 Review exercise for chapter 7

 

8. QUALITY OF TESTS

8.1 Type I and Type II errors

8.2 Finding Type I and Type II errors using the normal distribution

8.3 Calculate the size and power of a test

8.4 The power function

8.5 Mixed exercise 8

8.6 Review exercise for chapter 8

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