Formal Methods II

Expectation Functions or operators

Law of large numbers.
In a statistical context, laws of large numbers imply that the average of a random sample from a large population is likely to be close to the mean of the whole population.
(WPedia)

Binomial Distribution
Coin tosses
random bit strings
computer storage
computer programs (when translated into computer programs)

"In probability theory and statistics, the binomial distribution is the discrete probability distribution of the number of successes in a sequence of n independent yes/no experiments, each of which yields success with probability p. Such a success/failure experiment is also called a Bernoulli experiment or Bernoulli trial. In fact, when n = 1, then the binomial distribution is the Bernoulli distribution. The binomial distribution is the basis for the popular binomial test of statistical significance."
WP

B(n, p)

poisson Distribution
The number of visitors to a web page, the number of objects sent in a Java program.
The sole parameter is Lambda.
Lambda = 5:
Means that the poisson peaks on 5.

Uniform Distributions (the most boring!)
Can have a discreet case or continuous case.

Normal Distribution


The central limit therom shows that when you're modeling preactically anything you can get the mean (which is usually the most important thing you want).


Pseudo-random Numbers
We live as CS students in the land of fake - so we have to somehow generate random numbers for our simulations.