1. Lecture 2 Discrete Random Variables Section 2.1-2.4

2. Definition Each observation of an experiment is a random variable. (e.g. X) The set of possible values of a random variable is called the range of a random variable. (e.g. S X )

3. A random variable can be a function of the observation.

4. A random variable can be a function of another random variable

5. English translation: {X=x} emphasizes the idea that there is a set of sample points s within S (the sample space) for which X(s)=x.

6. Probability Mass Function

8. Families of Discrete Random Variables Bernoulli Random Variable Geometric Random Variable Binomial Random Variable Pascal Random Variable Discrete Uniform Random Variable (Not Covered) Poisson Random Variable

9. Bernoulli Random Variable

10. Examples of a Bernoulli Random Variable (1)

11. bernoullipmf(p,x)

12. Geometric Random Variable

13. Geometric RV Example (1)

14. geometricpmf(p,x)

15. Binomial Random Variable

16. Binomial RV Example (1)

17. binomialpmf(n,p,x)

18. Pascal Random Variable

19. Pascal Random Variable Example

20. Pascalpmf(k,p,x)

21. Poisson Random Variable

22. An Example of Poisson Random Variable

23. poinsonpmf(alpha,x)

24. An Example of Poisson Random Variable

27. CDF

28. CDF Example

29. geometricdf(p,x) What is the probability that Y is greater than 3?

30. poissoncdf(alpha,x) What is the probability that the switching office receives more than 2 calls, but less than 10 calls?