Contribution to E(X)

• Average 3.0 events per time period? That's your expected count
• Over 100 periods? Expect total ≈ 300 events
• Typical range per period: 1 to 5 events

What Does E(X) Mean?

The expected value E(X) represents the average number of events occurring in a fixed interval of time or space. For Poisson, this is simply λ - the rate parameter. If λ = 3, you expect 3 events per interval on average.

Interpreting Your Result

With E(X) = 3.00, this means:

• Expect 3.00 events per time interval
• Standard deviation is √λ = 1.73
• Most intervals have 1-5 events

Real-World Examples

• Phone calls (λ=2.5): Expect 2.5 calls per hour
• Website visits (λ=10): Expect 10 visits per minute
• Defects (λ=0.5): Expect 0.5 defects per batch
• Emails (λ=15): Expect 15 emails per day

Why E(X) = λ

The Poisson distribution models rare, random events occurring at a constant average rate. The parameter λ represents this rate - the expected number of occurrences. By definition, if the average rate is λ, then the expected value IS λ. No calculation needed - it is built into the definition of the distribution!