Poisson Distribution (Discrete)¶
Models the probability of a given number of events (\(k\)) occurring in a fixed interval of time or space, if events happen with a known constant mean rate (\(\lambda\)).
- Function: PMF
- Formula: \(P(X = k) = \frac{e^{-\lambda} \cdot \lambda^{k}}{k!}\)
- Parameter \(\lambda\): Expected number of events in the interval (Mean rate).
Use Case & Example:
| Scenario | Question | \(\lambda\) |
|---|---|---|
| Service | What is the probability of exactly 5 calls arriving at the call center in the next minute, if the average rate (\(\lambda\)) is 3 calls per minute? | \(3\) |
| Manufacturing | How likely are we to find 2 defects on a 100-meter length of wire, if the average defect rate is 0.5 per 100 meters? | \(0.5\) |