If X is a fair six-sided die, what is E[X]?

If X is a fair six-sided die, what is E[X]?

• A. 2.5
• B. 3.0
• C. 3.5
• D. 4.0

Answer: (C)

With a fair six-sided die, each face 1 through 6 is equally likely, so the expected value is the average of the possible outcomes weighted by their probabilities. Compute E[X] as (1/6) × (1 + 2 + 3 + 4 + 5 + 6) = 21/6 = 3.5. This represents the long-run average you’d expect if you rolled the die many times. Note that 3.5 isn’t a possible result of a single roll, but it is the precise mean of the distribution.

With a fair six-sided die, each face 1 through 6 is equally likely, so the expected value is the average of the possible outcomes weighted by their probabilities. Compute E[X] as (1/6) × (1 + 2 + 3 + 4 + 5 + 6) = 21/6 = 3.5. This represents the long-run average you’d expect if you rolled the die many times. Note that 3.5 isn’t a possible result of a single roll, but it is the precise mean of the distribution.