Topic 9 - Probability

Random

of or characterizing a process of selection in which each item of a set has an equal probability of being chosen.

Probability

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

Independence

The outcome of one trial must not influence the outcome of another.

Random Phenomenon

Outcomes that we cannot predict but that nonetheless have a regular distribution in many repetitions.

Sample Space (S)

In a random phenomenon, it is the set of all possible outcomes.

Event

An outcome or a set of outcomes of a random phenomenon.

Disjoint Events

Events A and B have no outcomes in common.

Independent Events

When events A and B occur, one event does not change the probability of the other.

Continuous Random Variable

A random variable that may assume any numerical value within the range of values.

Density Curve

A curve that is on or above the horizontal axis and has an area of exactly one underneath it.

Discrete Random Variable

A random variable that can take one of a finite number of distinct outcomes.

Probability Distribution

Lists the values and their respective probabilities.

Probability Histogram

A graph of the probability distribution that divides the range of possible values into classes or groups.

Random Variable

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

Uniform Distribution

A density curve with a height of 1, ranging from 0 to 1.

Binomial Setting

Given a fixed number of independent observations where each observation falls into 'success' or 'failure'.

Binomial Random Variable

The random variable X = number of successes in a binomial setting.

Binomial Distribution

Given parameters n and p, is the distribution of the count X of successes in the binomial setting.

Probability Distribution Function (PDF)

Assigns a probability to each value of X.

Cumulative Distribution Function (CDF)

Assigns the sum of probabilities for values less than or equal to X.

Binomial Coefficient

The number of ways of arranging k successes among n observations.

Binomial Probability

If X has the binomial distribution with n observations and probability p of success.

Union (U) of Events

Contains all outcomes in A, in B, or in both A and B.

Joint Event

The simultaneous occurrence of two events.

Joint Probability

The probability of a joint event.

Conditional Probability

Gives the probability of one event under the condition that we know another event.

Intersection (N)

Contains all outcomes that are in both A and B.

Complement of Event (A^c)

The event that A does not occur.