Probability Definitions Dr. Dan Gilbert Associate 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 estimate Event  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 ‌ ; not /

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 )

Definitions – Chapter 5 Random Variable  A variable whose numerical value is determined by the outcome of a random experiment Discrete 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