Contribution to E(X)

• Flipping 10 coins? Expect 5.0 heads on average
• Repeat this 10-flip experiment 100 times? Expect total ≈ 500 heads
• Each trial gives 5.0 ± 1.6 heads typically

What Does E(X) Mean?

The expected value E(X) represents the average number of successes you would get if you repeated this n-trial experiment many times. It is the 'center' of the distribution and the most likely outcome range.

Interpreting Your Result

With E(X) = 5.00, this means:

• Expect 5.00 successes per experiment on average
• Over many experiments, successes average to 5.00
• This is your 'break-even' point for planning or prediction

Real-World Examples

• 10 coin flips (p=0.5): E(X) = 5 heads expected
• 100 quality tests (p=0.02): E(X) = 2 defects expected
• 20 sales calls (p=0.3): E(X) = 6 sales expected

Why E(X) = n × p

Each of the n trials contributes p successes on average. Since trials are independent, you simply add up these contributions: n × p. This is the fundamental property of linearity of expectation.