Lecture Notes on Random Variables

Flashcards from Lecture Notes

Random Variable

Assigns a numerical value to each outcome in a sample space.

Discrete Random Variable

A random variable whose possible values form a discrete set, meaning there's a gap between each value.

Probability Mass Function (pmf)

A function, p(x) = P(X = x), describing the probability of possible values of a discrete random variable X.

Cumulative Distribution Function (cdf)

A function, F(x) = P(X <= x), specifying the probability that a random variable is less than or equal to a given value.

Mean of a Discrete Random Variable

μ = ΣxP(X = x), the sum of each possible value of X multiplied by its probability.

Variance of a Discrete Random Variable

σ^2 = Σ(x - μ)^2 * P(X = x), the sum of the squared differences between each value of X and the mean, weighted by their probabilities.

Standard Deviation

The square root of the variance.

Random Experiment

An experiment that results in different outcomes each time it is repeated under virtually identical conditions.

Sample Space

The set of all possible outcomes of a random experiment.