Bus Analytics Ch 4

Probability principles are the foundation for:

• Probability distributions.

• Mathematical expectation.

• Binomial and Poisson distributions.

sample space

The Collection Of All Possible Outcomes Of A Variable

• e.g. All 6 faces of a die:

• e.g. All 52 cards of a bridge deck 

simple event

An event described by a single characteristic.

• e.g., A day in January from all days in 2018.

joint event

An event described by two or more characteristics.

• e.g. A day in January that is also a Wednesday from all days in 2018.

complement of an event A (denotef A’)

All events that are not part of event A.

• e.g., All days from 2018 that are not in January.

probability

the numerical value representing the chance, likelihood, or possibility that a certain event will occur (always between 0 and 1).

impossible event

an event that has no chance of occurring (probability = 0).

certain event

an event that is sure to occur (probability = 1).

Mutually exclusive events

Events that cannot occur simultaneously.

collectively exhaustive events

• One of the events must occur.

• The set of events covers the entire sample space.

priori probability

based on prior knowledge of the process

empirical probability

based on observed data

subjetive probability

based on a combination of an individual’s past experience, personal opinion, and analysis of a particular situation.

• useful in situations when an empirical or a priori probability cannot be computed.

simple probability

refers to the probability of a simple event.

joint probability

refers to the probability of an occurrence of two or more events

probability

the numerical measure of the likelihood that an event will occur.

• The probability of any event must be between 0 and 1, inclusively.

conditional probability

the probability of one event, given that another event has occurred:

independent events

independent when the probability of one event is not affected by the fact that the other event has occurred.

bayes theorem

used to revise previously calculated probabilities based on new information.

counting rules

Rules for counting the number of possible outcomes