Quote Originally Posted by ScottS View Post
And thus "Expected Value" has no meaning?
Most random variables (r.v.s) have an expected value defined as its first moment. Those random variables that do not (e.g. a Cauchy r.v.) usually do not have one because the integral or sum defining its first moment is not defined mathematically (e.g. non-finite integral).

The random variable that arises from throwing a (fair) die and recording the number on the upper face is usually how most intro. probability courses explain it. If X denotes the r.v., it can take values 1, 2, ...., 6, each with probability of occurrence on any one throw of 1/6. So 1/6th of the time we'd expect to get a 1, 1/6th of the time a 2 and so on. The expected value of X is therefore 1/6(1+2+3+4+5+6) = 21/6 = 3.5. When the r.v. takes any value in a continuum (as opposed to a discrete or countably infinite set) the sum becomes an integral.

So anyway, just because something is random does not mean we can't do anything with it.

James.