Statistics Chapter 4

Sample Space

All the possible outcomes, or results, of an experiment. The sample space for our single-die experiment is the numbers {1,2,3,4,5,6}. Statisticians put the numbers in braces to signal that they represent the sample space.

Simple Event

An event with a single outcome in its most basic form that cannot be simplified. An example of a simple event is rolling a five with a single die.

Event

One or more outcomes of an experiment. The outcome, or outcomes, is a subset of the sample space. An example of an event is rolling a pair with two dice.

Multiplication Rule

a rule used to determine the probability of the intersection of two events

Mutually Exclusive

Two events are considered this if they cannot occur at the same time during an experiment

Probability

a numerical value ranging from 0 to 1. It indicates the chance, or likelihood, of a specific even occurring. If there is no chance of the event occurring, the probability is 0. If the event is absolutely going to occur, the probability of it occurring is 1.

Marginal Probability

another term used for simple probability

Addition Rule

for probabilities is used to calculate the probability of the union of events, that is, the probability that Event A, or Event B, or both events will occur

Dependent

if the occurrence of one event affects the occurrence of another event

Contingency Table

indicates the number of occurrences of events that are classified according to two categorical variables

Empirical Probability

involves conducting an experiment to observe the frequency with which an event occurs. (Frequency in which Event A occurs/Total number of observations)

Intersection

of Events A and B represents the number of instances in which Events A and B occur at the same time (that is, the same phone call is both from Christin and a crisis)

Union

of Events A and B represents the number of instances where either Event A or B occur or both events occur together

Simple Probability

represents the likelihood of a single (simple) event by occurring by itself

Permutations

the number of different ways in which objects can be arranged in order

Combinations

the number of different ways in which objects can be arranged without regard to order

Independent

the occurrence of one event has no impact on the occurrence of the other event

Prior Probability

the probability of Event A occurring as determined without any additional information that could influence the event

Experiment

the process of measuring or observing an activity for the purpose of collecting data. An example is rolling a sing six-sided die.

Complement

to Event A is defined as all the outcomes in the sample space that are not part of Event A and is denoted as A'

Bayes' Theorem

used to update prior probabilities with new information

Classical Probability

used when we know the number of possible outcomes of the event of interest and can calculate the probability of that event using Equation 1. (number of outcomes that constitute event A/total number of possible outcomes in the sample space)

Subjective Probability

when classical and empirical probabilities are not available and instead we rely on experience and intuition to estimate the probabilities

Collectively Exhaustive

a sample space is described as this if it includes every possible single event that can occur

Law of Large Numbers

states that when an experiment is conducted a large number of times, the empirical probabilities of the process will converge to the classical probabilities

Conditional Probability

the probability of Event A occurring, given the condition that Event B has occurred

Posterior Probability

which is a revision of the prior probability using additional information