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Probability

A value between zero and one, inclusive, describing the relative possibility an event will occur

Experiment

A process that leads to the occurence of one and only one of several possible observations

Outcome

A particular result of an experiment

Event

A collection of one or more outcomes of an experiment

Mutually Exclusive

The occurence of one event means that none of the other events can occur at the same time

Collectively Exhaustive

At least one of the events must occur when an experiment is conducted

Empirical or Relative Frequency

The probability of an event happening is the fraction of the time similar events happened in the past

Empirical Probability= # of Times Event Occurs/Total Number of Observations

Empirical Probability= # of Times Event Occurs/Total Number of Observations

Law of Large Numbers

Over a large number of trials, the empirical probability of an event will approach its true probability

Subjective Probability

The likelihood of a particular event happening that is assigned by an individual based on whatever information is available

Special Rule of Addition

P(A or B) = P(A) + P(B)

Compliment Rule

P(A)= 1-P(~A)

Joint Probability

A probability that measures the likelihood two or more events will happen concurrently

General Rule of Addition

P(A or B) = P(A) + P(B) -P(A and B)

Independence

The occurence of one event has no effect on the probability of the occurence of another event

Special Rule of Multiplication

P(A and B) = P(A)P(B)

Conditional Probability

The probability of a particular event occurring, given that another event has occurred

General Rule of Multiplication

P(A and B) = P(A)P(B/A)

Contingency Table

A table used to classify sample observations according to two or more identifiable characteristics

Prior Probability

The initial probability based on the present level of information

Posterior Probability

A revised probabilty based on additional information

Multiplication Formula

If there are m ways of doing one thing and n ways of doing another thing, there are m x n ways of doing both

Permutation

Any arrangement of x objects selected from a single group of n possible objects

Probability Distribution

A listing of all the outcomes of an experiment and the probability associated with each outcome

Characteristics of a Probability Distribution

1) The probability of a particular outcome is between 0 and 1

2) Outcomes are mutually exclusive events

3) The list is exhaustive- Sum of probabilities is 1

2) Outcomes are mutually exclusive events

3) The list is exhaustive- Sum of probabilities is 1

Random Variable

A quantity resulting from an experiment that, by chance, can assume different values

Discrete Random Variable

A random variable that can assume only certain clearly separated values

Mean of a Probability Distribution

The sum of x values times probability of its outcome

Variance of a Probability Distribution

Sum of (X values minus the mean) squared times the values expected probability

Uniform Probability Distribution

Rectangular in shape and is defined by minimum and maximum values

Normal Probability Distribution

Bell-Shaped, Symmetrical, Asymptotic (Closer and closer to the x axis but never touches it)

Z Value

The signed distance between a selected value, designated X, and the mean, divided by the standard deviation(X-Mean/Standard Deviation)

Binomial Probability Distribution

Widely occurring discrete probability distribution

4 Characteristics of a Probability Distribution

1) Outcome on each trial of an experiment either success of failure

2) Random variable counts the number of successes in a fixed number of trials

3) Probability of success and failure stay same for each trial

4) Trials are independent

2) Random variable counts the number of successes in a fixed number of trials

3) Probability of success and failure stay same for each trial

4) Trials are independent

Hypergeometric Probability Distribution

When probability of success does not remain teh same from trial to trial

4 Characteristics Hypergeometric Probability Distribution

1) Outcome on each trial of an experiment either a success or failure

2) Random variable is number of successes in a fixed number of trials

3) Trials are not independent

4) Proability of a success changes for each trial

2) Random variable is number of successes in a fixed number of trials

3) Trials are not independent

4) Proability of a success changes for each trial

Poisson Probability Distribution

Describes the number of times some event occurs during a specified interval

3 Characteristics of a Poisson Probability Experiment

1) Random Variable is number of times some event occurs during a defined interval

2) Probability of the event is proportional to size of the interval

3) Intervals do not overlap and are independent

2) Probability of the event is proportional to size of the interval

3) Intervals do not overlap and are independent

Tree Diagram

Graph that is helpful in organizing calculations that involve several stages

Bayes Theorem

Formula to arrive at the probability God does exist based on evidence available to him on earth