STOR 435: Introduction to Probability, Spring 2008


Study Guide for Midterm 1


1. Basics of counting: combinations and permutations, the binomial theorem.

2. Basic rules of Boolean algebra.

3. Axioms of probability and their immediate consequences (e.g. inclusion-exclusion).

4. Sample spaces with equally likely outcomes.

5. Conditional probability: basic definition and properties.

6. Disjoint events and partitions. 

7. The multiplication rule, law of total probability and Bayes' formula.

8. Conditional probabilities are probabilities when the conditioning event is fixed.

9. Definition and basic properties of independence.  Disjoint is different from independent.

10. Random variables: definition, ways of finding probabilities, ``when''

11. Discrete random variables: possible values and probability mass function.

12. Expectation of a discrete random variable: definition and basic properties

13. How to find the distribution of a function of a random variable.

14. How to find the expectation of a function of a random variable.

15. Variances: definition and basic properties.

16. Bernoulli trials

17. Binomial, geometric and negative binomial random variables: definition, pmf, expectation, variance

18. Poisson random variable: pmf, interpretation, application.