The expected value of a random variable is the "most likely" value the random variable will take. In the discrete case it's the mean value of the random variables possible values, and the continuous version can be thought of as the same for a continuous random variable. The expected value of a random variable is usually denoted as .

Formula

Discrete Case

For a discrete random variable (ie. a randomized dice that can only be the integers 1-6):

Where the sum is taken over all possible values of and is the probability that the random variable takes the value of .

Continuous Case

For a continuous random variable: