Chapter 5 Vocab

A variable whose value is a numerical outcome of a random phenomemon.

Random Variable (x)

Takes on all values in an interval of numbers. The probability distribution of Y is described by a density curve. The probability of any event is the area under the density curve and above the values of Y that make up the event.

Continuous Probability Model

General Multiplication Rule (for any two events)

P(A and B) = P(A) • P(B | A)

The set of all possible outcomes of a chance scenario.

Sample Space (S)

Compliment Rule

P(A does not occur) = 1 – P(A)

The probability that one event happens P(B) given that another event P(A) is already known to have happened.

Conditional Probability

Addition Rule for Disjoint Events

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

An outcome or a set of outcomes of a random phenomenon. A subset of the sample space.

Event

Multiplication Rule for Independent Events

P(A and B) = P(A) × P(B)

When two events share no outcomes in common, or no 'overlap'. Mutually exclusive.

ex) You can’t be a freshmen and a senior at the same time

Disjoint Events

A mathematical description of some chance process that consists of two parts: a sample space S and an assigned probability for each outcome.

Probability Model

Proof that Events A and B are Independent

P(B|A) = P(B)

A way to list all possible outcomes for a random variable and assign probabilities to each one. All probabilities must be between 0 and 1, and add up to 1.

Discrete Probability Model

A scenario where individual outcomes are uncertain but there is nonetheless a regular distribution of outcomes in a large number of repetitions.

Random Phenomenon

A way to list the sample space S of a chance behavior that involves a sequence of outcomes. A visual representation of the sample space that allows you to calculate each outcome by tracing it's path. Each branch represents a separate event's outcome.

Tree Diagram

How to calculate the probability that B happens, given that A occurs first. (Conditional Probability)

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

The proportion of times the outcome would occur in a very long series of repetitions.

Probability (P)

The chances of one event occurring are not affected by previous events in the series.

ex) being a senior and a girl

Independent Events

General Addition Rule (for any two events)

P(A or B) = P(A) + P(B) – P(A and B)

The tendency to get different outcomes when taking samples using the same probability and the same number of trials.

Chance Variability

U

either (add)

∩

Both (what they have in common)

A|B

given that

A^c

not including A

and

multiply

or

add

A set of outcomes

events (E)