Measures of Central Tendency

Consider the following statements regarding the Expected Value of a discrete random variable:

Statement I: The Expected Value mathematically represents the theoretical long-run arithmetic mean that would be obtained if a random experiment were repeated an infinite number of times.

Statement II: The Expected Value is calculated by taking the sum of the products of each possible outcome value multiplied by its corresponding probability.

Statement III: The Expected Value of a random variable is mathematically identical to the variance of its distribution.

Which of the statements are correct?