Contribution to E(X)

• Rolling once? Expect 3.5 on average
• Rolling 100 times? Expect total ≈ 350 (3.5 × 100)
• Rolling 1000 times? Expect total ≈ 3500

What Does E(X) Mean?

The expected value E(X) represents the average outcome you would get if you repeated this random experiment many times. For a discrete uniform distribution with equally likely outcomes, E(X) is simply the midpoint between the minimum and maximum values.

Interpreting Your Result

With E(X) = 3.50, this means:

• Over many trials, outcomes average to 3.50
• This is the 'center' of the distribution
• All values are equally likely, so E(X) is the midpoint

Real-World Examples

• Fair die (1-6): E(X) = 3.5 average per roll
• Random selection (1-100): E(X) = 50.5 on average
• Lottery numbers (10-20): E(X) = 15 expected value

Why E(X) = (a + b) / 2

Because every outcome has equal probability (1/n), the expected value calculation simplifies to the arithmetic mean of all values. The sum of integers from a to b equals n(a+b)/2, and dividing by n gives us (a+b)/2.