Question

Consider the probability distribution of a random variable x. is the expected value of the distribution necessarily one of the possible values of x?

Answer 1

No. The expected value can be a value different from the exact value of x.

Answer 2

The expected value of a distribution is considered as a mean, or average, for a probability distribution. It represents the center of the possible values of a variable. That doesn't necessarily mean it would be one of the possible values of x.