1. CSE 221: Probabilistic Analysis of Computer Systems Topics covered: Special discrete distributions Sec. 2.5.1.-2.5.4

2. Bernoulli pmf  What is a Bernoulli trial?  Sample space:  Bernoulli random variable:

3. Bernoulli pmf (contd..)  pmf:  Distribution function:  Parameters:

4. Bernoulli pmf (contd..)  Where to use:  Example: Tossing a biased coin.

5. Binomial pmf  Relationship between Bernoulli and Binomial random variables:  Sample space:  Definition of Binomial random variable:

6. Binomial pmf (contd..)  pmf:  Distribution function:  Parameters of a Binomial distribution:

7. Binomial pmf (contd..)  Where to use:  Example: Sequence of three coin tosses:

8. Geometric pmf  Relation between Bernoulli and Geometric pmf:  Sample space:  Definition of Geometric pmf:

9. Geometric pmf (contd..)  pmf:  Distribution function:  Parameters of a Geometric distribution:

10. Modified geometric pmf  Relation between Bernoulli pmf, geometric pmf and modified geometric pmf:  Sample space:  Definition of modified geometric pmf:

11. Modified geometric pmf (contd..)  pmf:  Distribution function:  Parameters of a modified geometric distribution:

12. Modified geometric pmf (contd..)  Where to use:  Example:

13. Geometric distribution: Memoryless property  Definition: