Question 609899
Intuitively, expected value is the value that you "expect" to obtain for a trial involving a random variable (or the average value if you repeat this trial indefinitely). For example, if you have a 1/100 chance of winning $200 and a 99/100 chance of losing $5 in a bet, your expected value is


(1/100)(200) + (99/100)(-5) = -2.95


This means that you expect to lose 2.95 on average.


The expected value is defined as


*[tex \LARGE E(x) = \sum xP(x)], in other words, the weighted average of the probabilities. Note that the random variable has to be numerical, e.g. P(6 on a die roll), not P(boy).