Principles of Probability and Discrete Probability Distributions

PROBABILITY

- quantitative measure of uncertainty

- a number that expresses the strength of our belief in the

occurrence of an uncertain event

Random Experiment

-any process that can be repeated under basically same

conditions and which yields well-defined outcomes

Sample space

set of all possible outcomes of a random experiment

Sample point

an element of the sample space

Elementary Event

event having one sample point

Compound Event

event containing more than one sample point

Impossible Event

- null space or null set

- event with no sample point

Priori

• assumes that all the sample points in S have equal

chances of occurring

• can be determined even without actually performing

the experiment

Posteriori

Based on experimental evidence

Law of Large Numbers

as an experiment is repeated again and again that is as n → ∞

A Posteriori probability → A Priori probability

Subjective Approach

guessed or estimated probability based on knowledge of relevant circumstances

Random Variable

variable that has a single numerical value (determined by chance) for

each outcome of a random experiment

Probability Distribution

listing of distinct outcomes of a random variable along with its associated probabilities

Cumulative Probability

measures the probability of more than one event

Uniform Distribution

• simplest of all the discrete probability distributions

• rectangular distribution

• random variable X assumes all its values with

equal probabilities

Binomial Distribution

a) The experiment consist of n repeated trials

b) Each trial results in an outcome that may be

classified as a success and a failure

c) The probability of success, denoted by p, remains

constant from trial to trial

d) The repeated trials are independent

Poisson Distribution

models the number of occurrences per unit time or space