CSE 221: Probabilistic Analysis of Computer Systems Topics covered: Special discrete distributions Sec

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

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

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

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

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

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

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

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

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

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

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

Geometric distribution: Memoryless property  Definition: