STOR 435: Introduction to Probability, Study Guide for the Final Exam


Combine Study Guides for Midterms 1 and II with the following

1. Definition of Eg(X,Y) in discrete and continuous cases

2. Basic properties of expectations: monotonicity and linearity

3. Method of indicator functions, including basic properties of indicator random variables

4. Sample mean of n random variables: definition, mean and variance

5. Independence and the expectation of products

6. Covariance: definition and basic properties

7. Correlation: definition and basic properties

8. Moment generating functions: definition and basic properties

9. Markov, Chebyshev and One-sided Chebyshev inequalities

10. Weak and strong laws of large numbers

11. Central limit theorem: ``A standardized sum of n i.i.d. random variables with finite second moment is approximately normal when n is large''.

12. Jensen's inequality

13. Cauchy-Schwartz inequality

14. Chernoff bound

15. Hoeffding's inequality