Question 1

How is the Poisson distribution related to the binomial?

Accepted Answer

The Poisson distribution is the limiting case of the binomial when n → ∞ and p → 0 while np stays fixed at λ.

Question 2

What does it mean that the variance equals the mean?

Accepted Answer

This property (equidispersion) means real data more spread out than their mean (overdispersion) will make a plain Poisson model understate the true variability.

Question 3

Can λ be a decimal, like 2.5 events per hour?

Accepted Answer

Yes — λ is an average rate and is often not a whole number. Only the outcome k must be a whole number.

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