CSE 3504: Probabilistic Analysis of Computer Systems Topics covered: Moments and transforms of special distributions (Sec ,4.5.3,4.5.4,4.5.5,4.5.6)

Bernoulli pmf  Description:  Expectation:  Variance:  Generating function:

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

Binomial pmf  Description:  Expectation:  Variance:  Generating function:

Binomial pmf (contd..)  Example: Number of heads in a sequence of three tosses of a biased coin.

Geometric pmf  Description:  Expectation:  Variance:  Probability generating function:

Geometric pmf (contd..)  Example: Coin tosses of a biased coin, number of tails until the first head.

Poisson pmf  Description:  Expectation:  Variance:  Probability generating function:

Poisson pmf (contd..)  Example: Arrival of jobs in a queue.

Uniform distribution  Definition:  Expectation:  Variance:  Laplace-Stilje’s transform:

Uniform distribution (contd..)  Example: Rainfall on a given day.