Statistics - C4

A sample point refers to a(n)

individual outcome of an experiment

The set of all possible sample points (experimental outcomes) is called

the sample space

A graphical device used for enumerating sample points in a multiple-step experiment is a

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When the results of experimentation or historical data are used to assign probability values, the method used to assign probabilities is referred to as the

relative frequency method

A graphical method of representing the sample points of a multiple-step experiment is

a tree diagram

Given that event E has a probability of .25, the probability of the complement of event E

must be 0.75

The union of events A and B is the event containing

all the sample points belong to A or B or both

Probability

A numerical measure of the likelihood than an event will occur

Experiment

A process that generates well-defined outcomes

Sample Space

the set of all experimental outcomes

Sample point

An element of the sample space. A sample point represents an experiment outcome.

Tree diagram

A graphical representation that helps in visualizing a multiple-step experiment

Classical method

A method of assigning probabilites that is appropriate when all experimental outcomes are equally likely

Relative frequency method

A method of assigning probabilities that is appropriate when data are available to estimate the proportion of the time the experimental outcome will occur if the experiment is repeated a large number of times

Subjective method

A method of assigning probabilities on the basis of judgment

Event

A collectiion of sample points.

Complement of A

The event consisting of all sample points that are not in A

Venn diagram

A graphical representation for showing symbolically the sample space and operatons involving events in which the sample space is represented by a rectangle and events are represented as circles within the sample space

Union of A and B

The event containing all sample points belonging to A or B or both. The union is denoted A U B.

Intersection of A and B

The event containing the sample points belonging to both A and B. The intersection is denoted A n B.

Addition law

A probability law used to compute the probability of the union of two events. It is P(A U B) = P(A) + P(B) - P(A n b). For mutually exclusive events, P(A n B) = 0; in this case the addition law reduces to P(A U B) = P(A) + P(B).

Mutually Exclusive Events

Events that have no sample points in common; that is, A n B is empty and P(A n B) = 0.

Conditional Probability

The probability of an event given that another event ialready occured. The conditional probability of A given B is P(A | B) = P(A n B)/P(B)

Joint Probability

The probability of two events both occurring; that is, the probability of the intersection of two events.

Marginal Probability

The values in the margins of a joint probability table that provide the probabilities of each event separately.

Independent events

Two events A and B where P(A | B) = P(A) or P(B | A) = P(B); that is, the events have no influence on each other

Multiplication Law

A brabilitiy law used to compute the probability of the itnersection of two events. It is P(A n b) - P(B)P(A | B) or P(A n B) = P(A)P(B | A). For independent events it reduces to P(A n B) = P(A)P(B).

Prior Probabilities

Initial estimates of the probabilities of events

Posterior Probabilities

Revised probabilities of events based on additional information.

Bayes'theorem

A method used to compute posterior probabilities.