State the Mean and Variance of a Poisson Count
Company: LinkedIn
Role: Data Scientist
Category: Statistics & Math
Difficulty: medium
Interview Round: Onsite
# State the Mean and Variance of a Poisson Count
If the number of arrivals in a fixed interval follows a Poisson distribution with parameter lambda, what are its mean and variance? Explain the relationship between the interval parameter and an arrival rate, and what this does and does not tell you about a queue.
### What a Strong Answer Covers
- Equality of the Poisson mean and variance to the interval parameter.
- Correct scaling of that parameter with interval length under a homogeneous arrival model.
- A distinction between arrival counts, interarrival times, and queue waiting time.
```hint Check the parameter’s units
A rate per minute and the expected count in a ten-minute interval are different quantities.
```
### Follow-up Questions
- What if observed count variance is much larger than its mean?
- Can the arrival rate alone determine expected waiting time?
Overview: Explain Poisson count mean and variance, rate-to-interval scaling, and the distinction between arrivals and queue waiting times.
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