Essentials of Probability for Statistics : A primer

I Basic Probability

1 What is probability?
1.1 Sample spaces and events
1.2 Probability measure
1.3 Counting methods
1.4 Probability of a Union
1.5 Exercises

2 Conditional Probability
2.1 Conditional probability
2.2 Law of total probability
2.3 Bayes’ theorem
2.4 Independent events
2.5 Exercises

3 Discrete random variables
3.1 Discrete random variables
3.2 Moments
3.3 Joint distributions
3.4 Waiting time distributions
3.5 Poisson distribution
3.6 Exercises

II Continuous Distributions

4 Continuous random variables
4.1 Continuous random variables
4.2 Moments
4.3 Normal distribution
4.4 Waiting time distributions
4.5 Beta distributions
4.6 Exercises

5 Joint distributions
5.1 Bivariate random variables
5.2 Independent random variables
5.3 Transformation of two random variables
5.4 Joint moments
5.5 Exercises

6 Conditional distributions
6.1 Conditional density
6.2 Conditional expectation
6.3 Conditional variance
6.4 Bivariate normal distributions
6.5 Multivariate distributions
6.6 Exercises