Contribution to E(X)

• 20% success rate? Expect 5.0 attempts until first success
• 100 experiments? Expect total ≈ 500 attempts
• Typical range: 1 to 9 attempts

What Does E(X) Mean?

The expected value E(X) represents the average number of trials you need until you get your first success. It is how many attempts you should expect before achieving success when each trial is independent.

Interpreting Your Result

With E(X) = 5.00, this means:

• Expect 5.00 trials until first success on average
• Half the time you will succeed within 4 trials (median)
• Each trial has the same probability - past failures do not affect future chances

Real-World Examples

• Coin flips (p=0.5): E(X) = 2 flips until heads
• Sales calls (p=0.1): E(X) = 10 calls until first sale
• Quality test (p=0.02): E(X) = 50 items until first defect

Why E(X) = 1 / p

The geometric distribution is memoryless - each trial is independent with success probability p. The expected waiting time is simply the reciprocal: if you have a 20% chance each trial (p=0.2), you expect to wait 1/0.2 = 5 trials on average.