f X is a random variable with possible outcomes 3 and 8, with  P( X = 3) = 0, then E(X) is

The expected value (E(X)) of a random variable is calculated as the sum of all possible outcomes each multiplied by their respective probabilities.

In this case, X can take on the values 3 and 8.

Given that P(X = 3) = 0, this means that the random variable X will never take on the value 3.

The only other possible outcome for X is 8. Since these are the only two possible outcomes, and X can't be 3, the probability that X = 8 must be 1 (because the sum of the probabilities of all possible outcomes must equal 1).

So, we can calculate E(X) as follows:

E(X) = (3 * P(X = 3)) + (8 * P(X = 8)) = (3 * 0) + (8 * 1) = 0 + 8 = 8

Therefore, E(X) = 8.