Poisson Distribution Calculator
P(X = x):
P(X < x):
P(X ≤ x):
P(X > x):
P(X ≥ x):
Understanding Poisson Distribution
The Poisson distribution models the probability of a specific number of events occurring in a fixed interval of time or space, assuming these events occur independently at a constant average rate.
Formula
P(X = k) = (λᵏ × e⁻λ) / k!
where:
λ (lambda) = average rate of success
k = number of successes
e = Euler's number (≈ 2.71828)
Common Applications
- Customer arrivals per hour
- Network traffic analysis
- Quality control in manufacturing
- Natural phenomena occurrence rates