Question 1

What is the Poisson distribution formula?

Accepted Answer

P(X = k) = (λ^k * e^(-λ)) / k!, where λ is the average rate of events, k is the number of occurrences, and e is Euler's number (~2.71828).

Question 2

What is the relationship between mean and variance in a Poisson distribution?

Accepted Answer

In a pure Poisson distribution, the mean and variance are equal (Mean = Variance = λ).

Question 3

When should you use a Poisson distribution instead of a Binomial distribution?

Accepted Answer

Use Poisson when counting the number of times an event occurs in a fixed interval of time or space, where the number of possible trials is infinite or unknown.

Question 4

Can lambda or k be negative?

Accepted Answer

No, lambda (average rate) must be greater than zero, and k (event count) must be a non-negative integer (0, 1, 2, ...).

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