ANOP Week 5

Flashcards covering key concepts from Chapter 5.1-5.4 of ANOP 102: Spreadsheet Modeling and Data Analysis, focusing on the introduction to probability, events, relationships of probability, and random variables.

Probability

The numerical measure of the likelihood that an event will occur.

Probability Distribution

A measure of uncertainty often communicated to help a decision maker evaluate possible actions.

Event

A collection of outcomes.

Random Experiment

A process that generates well-defined outcomes.

Sample Space

All possible outcomes for a random experiment.

Experimental Outcomes (Sample Points)

The individual results generated by a random experiment.

Probability of an Event

A value between 0 and 1 (inclusive), where a value of 1 implies the event will happen for sure. It is equal to the sum of probabilities of outcomes for the event.

Complement of an Event (A^C)

The event consisting of all outcomes that are not in event A. P(A) + P(A^C) = 1.

Intersection of Events (A
T B)

The event containing all outcomes belonging to both event A and event B (also denoted as "A and B").

Union of Events (A
U B)

The event containing all outcomes that are in event A, event B, or both (also denoted as "A or B").

Addition Law

A way to compute the probability of the union of two events: P(A
U B) = P(A) + P(B) - P(A
T B).

Mutually Exclusive Events

Two events that have no outcomes in common; if one event occurs, the other cannot. Their intersection probability P(A
T B) = 0.

Joint Probabilities

The intersection probabilities of events, typically found in a joint probability table.

Marginal Probabilities

The probabilities of each separate event, found at the bottom and right margins of a joint probability table, calculated as the sums of respective joint probabilities' rows and columns.

Conditional Probability (P(A|B))

The probability of event A, given that event B has occurred.

Independent Events

Events A and B are independent if P(A|B) = P(A) or P(B|A) = P(B). Two events with nonzero probabilities cannot be both mutually exclusive and independent.

Dependent Events

Events A and B are dependent if P(A|B)
T P(A) or P(B|A)
T P(B).

Multiplication Law

Provides a way to compute the probability of the intersection of two events: P(A
T B) = P(A|B)P(B) or P(B
T A) = P(B|A)P(A).

Multiplication Law for Independent Events

P(A
T B) = P(A)P(B).

Bayes’ Theorem

A method for revising probabilities when new information is obtained, using prior probabilities and conditional probabilities to calculate posterior probabilities.

Prior Probability

Initial probability estimates for specific events of interest before new information is obtained.

Posterior Probability

Revised probabilities calculated after new information about events is obtained.

Random Variable

A numerical description of the outcome of a random experiment.

Discrete Random Variable

A random variable that can take on only specified discrete values and a countable number of distinct values.

Continuous Random Variable

A random variable that may assume any numerical value in an interval or collection of intervals, such as values related to time, weight, distance, and temperature.