Example

Variance of linear functions lemma

Classic discrete distributions

Uniform distribution definition

In a uniform discrete distribution, every outcome is equally likely

Bernoulli distribution definition

Binomial distribution definition

Example

It is known that screws produced by a certain company will be defective with probability , independently of one another. The company sells the screws in packages of 10 and offers a money-back guarantee that at most 1 of the 10 screws is defective. What proportion of packages sold must the company replace?

Example

Player bets on one of the numbers 1 through 6. Three fair dice are rolled. For each dice, if the result is the same as player’s bet, player receives 1 unit. If none of the dice have the player’s bet, 1 unit is taken from the player. Is the game fair to the player?

Properties of Binomial distribution

Form of a binomial distribution

Poisson distribution definition

Approximation of a binomial distribution with a Poisson distribution