4.1.2—Expected values of functions

For a discrete random variable X, E(X)=ΣxP(X=x). It is the long-run mean of repeated trials and may be a value that no single outcome can take.

Check that probabilities sum to one before calculating. For a function g(X), use E[g(X)]=Σg(x)P(X=x), not generally g(E(X)).

If X is 0 or 2 with probabilities 0.7 and 0.3, E(X)=0.6; no individual trial has outcome 0.6. But over many trials the average approaches 0.6.

Expected value is not the most likely value and is not a promise about the next observation.