The *expectation* or *expected value* of a random variable
is denoted by . It can be considered as a kind of weighted
average for , in which the weights are obtained from the
probability distribution. If is discrete, then

(9.10) |

If is continuous, then

One can then define

Now consider tossing two dice in succession. Each element
is expressed as in which
. Since
, the random variable needs to be slightly more
interesting. One common approach is to count the sum of the dice,
which yields
for any . In this case, .

Steven M LaValle 2012-04-20