STAT1127-Probability Distributions

a table, graph, formula, or other device used to specify all possible values of a discrete random variable along with their respective probabilities.

probability distribution

2 essential properties

0<P(X=x)<1, sum of x P(X=x)=1

cumulative distribution

F(y)=P(X<x) sum of x<y P(X=x)

–For finite sample size

binomial

–For infinite (or large) sample size

poisson

•One of the most widely encountered probability distributions in applied statistics

•Derived from a process known as Bernoulli trial

binomial distribution

When a random process or experiment, called a trial, can result in only one of two mutually exclusive outcomes, such as dead or alive, sick or well

bernoulli trial

1.Each trial results in one of two possible, mutually exclusive, outcomes. One of the possible outcome is denoted (arbitrarily) as a success, and the other is denoted as a failure

2.The probability of a success, denoted by p, remains constant from trial to trial. The probability of a failure, 1-p, is denoted by q

3.The trials are independent; that is, the outcome of any particular trial is not affected by the outcome of any other trial.

bernoulli process

n objects taken k at a time is an unordered subset of k of the n objects.

combination

Out of n trials, the probability to observe k successes

binomial probability

•The table does not give probabilities for values of p greater than 0.5

when p>0.5

When p>0.5

observing k succeses, each with probability p; observing n-k failures, each with probability 1-p