4.3

This set of flashcards covers key concepts related to random variables, their types, and probability distributions.

Random Variable

A real-valued function defined on the sample space whose value is a numerical outcome of a random phenomenon.

Discrete Random Variable

A random variable that has a finite number of possible values.

Probability Distribution

Lists the values of a random variable and their corresponding probabilities.

Probability Conditions for Random Variables

Conditions that must be satisfied: 0 ≤ pi ≤ 1 and the sum of all probabilities equals 1.

Continuous Random Variable

A random variable that takes all values in an interval of numbers.

Density Curve

Describes the probability distribution of a continuous random variable.

Normal Distribution

An example of a continuous probability distribution characterized by data falling within a specific percentage range around the mean.

Uniform Distribution U[0,1]

A continuous probability distribution where all intervals of the same length within [0,1] have equal probabilities.

Area under the Density Curve

Represents the probability of an event for continuous random variables.

Event A

A specific occurrence in the context of probability, where the area under the density curve equals the probability of that event.