Statistics Chapter 4

Sample space

a complete roster or listing of all elementary events for an experiment

Experiment

a process that produces outcomes

complement

all the elementary events of an experiment not in X comprise its complement

Subjective method

based on the feelings or insights of the person determining the probability

collectively exhaustive events

contains all possible elementary events for an experiment

Intersection

contains the elements common to both sets

marginal probability

denoted P(E), where E is some event. computed by dividing some subtotal by the whole

joint probability table

displays the intersection (joint) probabilities along with the marginal probabilities of a given problem

Elementary events

events that cannot be decomposed or broken down into other events

mn counting rule

for an operation that can be done m ways and a second operation that can be done n ways, the two operations then can occur, in order, in mn ways. this rule can be extended to cases with three or more operations

Union

formed by combining elements of from each of the sets

independent events

if the occurrence or nonoccurrence of on of the events does not affect the occurrence or nonoccurrence of the other event

conditional probability

is denoted P(E1/E2). the probability that E1 will occur given that E2 is known to have occurred

union probability

is denoted P(E1UE2), where E1 and E2 are two events. it is the probability that E1 will occur or E2 will occur or that both E1 and E2 will occur

combinations

sampling n items from a population of size n without replacement

joint probability

the intersection of two events. denoted as P(E1nE2)

complement of a union

the probability of a union of two events X and Y represents the probability that the outcome is either X or it is Y or it is both X and Y

Relative frequency of occurrence method

the probability of an event occurring is equal to the number of times the event has occurred in the past divided by the total number of opportunities for the event to have occurred

Set notation

the use of braces to group numbers, is used as a symbolic tool for unions and intersections

mutually exclusive events

two or more events if the occurrence of one event precludes the occurrence of the other event(s)

Classical method of assigning probabilities

when probabilities are assigned based on laws and rules