Discrete Probability Distributions

These flashcards cover key concepts from the lecture notes on discrete probability distributions, including definitions of random variables, probability functions, and related financial applications.

Random Variable

A numerical description of the outcome of an experiment.

Discrete Random Variable

A random variable that may assume either a finite number of values or an infinite sequence of values.

Continuous Random Variable

A random variable that may assume any numerical value within an interval or collection of intervals.

Probability Distribution

Describes how probabilities are distributed over the values of a random variable.

Expected Value (μ)

A measure of the central location of a random variable, calculated as a weighted average of the values.

Variance (Var)

Summarizes the variability in the values of a random variable.

Standard Deviation (σ)

A measure of the amount of variation or dispersion of a set of values.

Sample Space (S)

The set of all possible outcomes of a random experiment.

Bivariate Probability Distribution

A probability distribution that involves two random variables.

Covariance

A measure of how much two random variables change together.

Probability Function

Defines the probability distribution by providing the probability for each value of the random variable.

Relative Frequency Method

A method used to develop discrete probability distributions based on observed frequencies.

Financial Portfolio

A collection of financial assets, such as stocks and bonds, held by an investor.

Risk

The potential financial loss or gain associated with an investment.

Linear Combination of Random Variables

A combination of two or more random variables, expressed as r = ax + by.