Statistics Chapter 4
Joint Probability
P(ANB)=P(AIB)P(B) or P(ANB)=P(BIA)P(A).
Experiment
A trial that results in one of several uncertain outcomes.
Dependent
A and B are ___ if and only if P(AIB) does not equal P(A) or P(BIA) does not equal P(B).
Independent
A and B are ___ if and only if P(AIB)=P(A) or P(BIA)=P(B).
Probability
A numerical value that measures the likelihood than an uncertain event occurs.
Joint Probability
A probability that A occurs given that B has occurred times the probability that B occurs.
Event
A subset of a sample space that can either be simple or have multiple outcomes.
Sample Space
An experiment contains all possible outcomes of the experiment.
A Priori Probability
Based on logical analysis rather than on observation or personal judgement.
Total Probability Rule
Expresses the unconditional probability of an event, P(A), in terms of probabilities conditional on various mutually exclusive and exhaustive events.
Contingency Table
Generally shows frequencies for two qualitative or categorical variables, x and y, where each cell represents a mutually exclusive combination of the pair of x and y values.
Bayes Theorem
Given a set of prior possibilities for an event of interest, upon the arrival of new information, the rule for updating the probability of the event is ___.
MRFIE
P(ANB)=P(A)P(B)
Complement Rule
States that the probability of the complement in an event is equal to one minus the probability of the event.
Factorial Formula
The calculation of the number of ways to assign every member of a group of size n to n slots.
Complement
The part of an event consisting of all outcomes in the sample space that are not in the event.
Conditional Probability
The probability of an event given that another event has already occurred.
Unconditional Propensity
The probability of an event without any restriction. (Stand-alone probability)
Multiplication Rule
The probability that A and B both occur.
Addition Rule
The probability that A or B occurs, or that at least one of these events occurs, is equal to the probability that A occurs, plus the probability that B occurs, minus the probability that both A and B occur.
Intersection
Two events consisting of all outcomes in A AND B. (ANB)
Union
Two events consisting of all outcomes in A OR B. (AUB)
Subjective Probability
Calculated by drawing on personal and subjective judgement.
Empirical Probability
Calculated from date as a relative frequency of occurrence.
Multiplication Rule for Independent Events
Dictates that the joint probability of A and B equals the product of the individual probabilities of A and B.
Exhaustive
Events that all possible outcomes of a random experiment are included in the events.
Mutually Exclusive
Events that do not share any common outcome of a random experiment.
Permutation Formula
The calculation of the number of ways to choose x objects from a total on n objects, where the order in which the x objects are listed does matter.
Combination Formula
The calculation of the number of ways to choose x objects from a total on n objects, where the order in which the x objects are listed does not matter.
Probability
a value between one and zero where the value of zero indicates impossible events and the value of one indicates definite events.