Lesson 5.4MathCode~40 min

Expected value

The long-run average of anything random — the quantity every model and every agent is quietly optimising.

Module 5 · 0/9 done

What happens on average

One roll of a die could be anything from 1 to 6. But roll it ten thousand times and the average settles down to something very predictable. That long-run average is the expected value. Work it out by weighting each outcome by its probability:

\mathbb{E}[X] = \sum_i p_i\,x_i

Fig 5.7Play a game over and over. The running average wobbles, then locks onto the expected value (dashed). This is the law of large numbers.