Discrete Random Variables

Discrete Random Variable

A numerical value assigned to each outcome of a random experiment.

Probability Distribution

A listing or function indicating the probability that a random variable X takes on each of its possible values.

Mean (E[X] or µ)

The weighted average of the possible values of a random variable, calculated using the probabilities as weights.

Variance (σ²)

A measure of the variability of a probability distribution, calculated as the expected value of the squared differences from the mean.

Standard Deviation (σ)

The square root of the variance, representing the average distance of each random variable value from the mean.

Total Probability Rule

The sum of the probabilities of all possible outcomes of a random variable must equal one.

Example of Coin Flips

A classic example used to illustrate discrete random variables, where the outcomes depend on the number of heads when flipping coins.

Risk Assessment in Games

Evaluating which game has higher variability in outcomes, indicated by the standard deviation.

Weights in Probability

The probabilities used to weight the average calculations for mean and variance in a probability distribution.