Econ 120A - Discrete Probability Distributions

Flashcards covering key vocabulary and concepts related to discrete probability distributions.

Random Variable

A mathematical function that assigns a real number to each outcome in the sample space of an experiment.

Discrete Random Variable

Random variables where we can list the possible values.

Continuous Random Variable

Random variables where we cannot list the possible values due to too many values.

Probability Distribution

An assignment of a probability to each possible value of the random variable.

Probability Notation

P(X=x) = p(x) = probability that the random variable X takes on the specific value x

Discrete Uniform Probability Distribution

The simplest example of a discrete probability distribution given by a formula, where each value is equally likely.

Basic Properties of Probability Distributions

0 ≤ p(x) ≤ 1 and σ 𝑝 𝑥 = 1

Mean of a Discrete Random Variable

𝜇 = σ 𝑥𝑝 𝑥; A weighted average of all possible values of X, where the weights are the probabilities of those values.

Variance of a Discrete Random Variable

𝜎2 = σ 𝑥 − 𝜇 2 𝑝 𝑥; A weighted average of squared deviations from the mean, where the weights are the probabilities of those values.

Population Mean

𝜇 = σ 𝑥𝑝 𝑥

Population Variance

𝜎2 = σ 𝑥 − 𝜇 2 𝑝 𝑥