Probability Definitions

Dr. Dan GilbertAssociate Professor

Tennessee Wesleyan College

Definitions

Probability The expected outcome of an activity A numerical statement about the likelihood that

an event will occur

Experiment An activity that produces an event

Sample The set of all possible outcomes of an

experiment

Definitions

Classical probability The number of outcomes favorable to the

occurrence of an event, divided by the number of possible outcomes

Subjective probability Probability based on personal beliefs of the

person making the probability estimateEvent

One or more of the possible outcomes of an experiment

Definitions

Mutually exclusive events Events which cannot happen together

Non-mutually exclusive events Events which may or may not occur

together

Definitions

Conditional probability The probability of one event occurring given

that another event has occurred.

Joint probability The probability of events occurring together or

in succession

Marginal probability The unconditional probability of one event

occurring

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Definitions

Statistical independence The conditions in which the occurrence of one

event has no effect upon the probability of any other event

Statistical dependence The conditions in which the probability of some

event is dependent upon or affected by the occurrence of some other event

P(A B) = P(A) +

P(B)

P(A B) = P(A) +

P(B)

Definitions – Chapter 5

Random Variable A variable whose numerical value is determined

by the outcome of a random experimentDiscrete Random Variable

A random variable whose value is obtained by some finite number

Continuous Random Variable A random variable whose value is obtained

from a continuous scale within a given interval, and has an infinite number of possible outcomes

Discrete vs Continuous

Discrete

Counting

Continuous

Measuring

Definitions

Probability Distribution A systematic listing of all the possible values a

random variable can take on, plus their respective probabilities

Discrete Probability Distribution A probability distribution in which the variable is

allowed to take on only a limited number of values

Expected value A measure of the central location of a random

variable

Definitions

Binomial probability distribution A discrete probability distribution of the results

of an experiment using the Bernoulli process

Bernoulli process A process in which

1) Each trial has only two possible outcomes

2) The probability of the outcome of any trial remains fixed over time

3) The trials are statistically independent

Definitions

Poisson probability distribution A discrete distribution in which the probability of

the occurrence of an event within a very small time period is very small, in which the probability of two or more events will occur within the same small time interval is effectively zero, and in which the probability of the occurrence of the event within one time period is independent of where that time period is.

Chapter 6

Continuous probability distribution A probability distribution in which the variable is

presented to take on any variable within a given range

Normal distribution A distribution in which the curve has a single

peak, in which it is bell-shaped, in which the mean lies at the center of the distribution, and in which the two tails extend indefinitely and never touch