Statistics Section 3 Flashcards

Questions and Answers

What is a random experiment?

An action that leads to one outcome

An action that leads to one of several possible outcomes (correct)

An event that cannot happen at the same time

A technique to compute probabilities

What does the classical approach to probability assume?

Each simple event has an equal chance of occurring

What is relative frequency approach?

The long-run frequency of an outcome's occurrence

What does the subjective approach to probability involve?

The degree of belief based on past observations Signup and view all the answers

What is joint probability?

The probability of the intersection of two events Signup and view all the answers

Define marginal probability.

Likelihood of a specific event occurring, regardless of other events Signup and view all the answers

What is conditional probability?

Probability of one event given another event has occurred Signup and view all the answers

What is the union of two events?

The event containing all sample points in either event or both Signup and view all the answers

What is the complement of event A?

The event that occurs when event A does not occur Signup and view all the answers

What is Bayes' Law used for?

To compute posterior probabilities Signup and view all the answers

How does the classical approach describe probability?

In terms of the expected proportion of an event's occurrence Signup and view all the answers

What does it mean if a set of events is exhaustive?

It includes all possible outcomes of an experiment Signup and view all the answers

What is the addition rule in probability?

The probability of mutually exclusive events is the sum of their probabilities. Signup and view all the answers

What are mutually exclusive events?

Events that cannot happen at the same time Signup and view all the answers

Study Notes

Key Concepts in Probability

Random Experiment: An action resulting in one of several possible outcomes that cannot be predicted with certainty.
Classical Approach to Probability: Assumes all outcomes are equally likely; for example, rolling a fair die gives each of the six faces a probability of 1/6.
Relative Frequency Approach: Estimates probability based on the long-term frequency of an outcome; for instance, if 200 out of 1000 students receive an A, the relative frequency is 20%.
Subjective Approach: Involves personal judgment and belief; an example includes weather forecasting, which combines previous data and current observations.

Types of Probability

Joint Probability: The probability of two events occurring simultaneously; it represents the intersection of those events.
Marginal Probability: Evaluates the likelihood of an event occurring without consideration of other events; it measures standalone probabilities.
Conditional Probability: The likelihood of one event occurring given that another has occurred; crucial for understanding dependent events.

Events and Their Relationships

Union of Two Events: Refers to the event consisting of all outcomes found in either event A or event B or both.
Complement of Event A: Represents outcomes where A does not happen; the sum of the probabilities of an event and its complement equals 1.

Advanced Probability Concepts

Bayes' Law: A formula used to calculate posterior probabilities, allowing for the update of the probability estimate based on new evidence.
Proportional Expectation in Classical Approach: Describes probability in terms of how often an outcome is expected to occur theoretically over numerous trials.
Exhaustive Events: A set of events that includes all possible outcomes of an experiment, providing complete coverage for probability assessments.

Rules and Classifications

Addition Rule: For mutually exclusive events, the probability that one or the other occurs is the sum of their individual probabilities.
Mutually Exclusive Events: Events that cannot occur at the same time; the occurrence of one excludes the others.

Description

This quiz covers key terms and definitions from Section 3 of your statistics study material. Test your understanding of concepts like random experiments, probability approaches, and more. Perfect for reviewing important terminology before exams.