MATH 350: Probability

Midterm Exam Review Topics

October 21, 2024

1. Approximating integrals (areas) and constants with the use of random numbers

2. Sample spaces; events; discrete vs. continuous random variables

3. Discrete random variables: finite and countably infinite probability distributions

4. Basic theorems about probability

5. Tree probability diagrams

6. Continuous random variables; density functions; cumulative distribution functions

7. Uniform and exponential continuous random variables

8. Obtaining one- and multi-dimensional probability distribution and density functions of random variables based on the U distribution CDF or with the use of geometry

9. The Birthday Problem

10. Permutations and k-permutations

11. Binomial coefficients; binomial theorem; Pascal triangle

12. Combinations; applications in card games

13. Bernoulli process and distribution; practical applications; "at least" and "at most" cases

14. Geometric distribution

15. Discrete conditional probabilities

16. Independence of events

17. Bayes' probabilities and Bayes' formula; applications

18. Joint discrete probability distributions

19. Independence of discrete random variables

20. Memoryless property of the exponential distribution; the "Bus Paradox"

21. Continuous joint distributions; joint continuous densities

22. Marginal densities; independence of joint continuous random variables

23. Poisson distribution and its derivation

24. Important continuous densities: uniform, exponential, normal (standard and non-standard)

25. Functions of random variables - derivation of density using the CDF method

26. Standard normal distribution; Z-table and its use in applications

27. Expected value of discrete and continuous random variables and functions of random variables

28. Expected value of Bernoulli, Poisson, and geometric random variables

29. Expected value of sums of random variables