SL 4.7—Discrete random variables

A discrete random variable assigns values to countable outcomes.

A discrete probability distribution lists countable values $x$ and probabilities $P(X=x)$ that sum to 1. Its expected value is $E(X)=\sum xP(X=x)$, a weighted long-run mean rather than a guaranteed single outcome.

Example

If X is 0,1,2 with probabilities .2,.5,.3, E(X)=0(.2)+1(.5)+2(.3)=1.1.

Check that all probabilities are non-negative and sum to 1, then calculate $E(X)=\sum xP(X=x)$. If $X$ is a player's gain, $E(X)=0$ describes a fair game in the long run.

Expected value need not be attainable in one play, and variance is not a required calculation in this specific SL 4.7 objective.