Which measure of a probability distribution's center is defined as the expected value of the random variable?

• A. Mode
• B. Median
• C. Expected Value
• D. Variance

Answer: (C)

The concept being tested is the expected value, which serves as the center of a probability distribution in the long run. For a discrete variable with values x_i and probabilities p_i, the center is E[X] = ∑ x_i p_i. For a continuous variable with density f, it’s E[X] = ∫ x f(x) dx. Intuitively, it’s the average outcome you’d expect if you could repeat the experiment many times. This differs from the mode (the most likely value) and the median (the middle value that splits probability mass); the expected value is a balancing average and may not coincide with either, especially in skewed distributions. Variance, in contrast, measures spread around that center, not the center itself.