Expected Values and Variance

The expected value and variance tell us a lot about the “personality” of a random variable.

The expected value is a measure of location – roughly speaking, where the random variable tends to hang out on average. The variance, and its close relative the standard deviation, instead tell us about spread – how far its possible values tend to lie from this average.

We begin by developing some intuition for these ideas, before looking at how to calculate expected values, variances and standard deviations. We then extend the same ideas from discrete to continuous random variables.

These quantities will appear almost everywhere in probability, statistics and econometrics, so we will get to know them very well!