Total typos across four pages

Question

A proofreader finds typos on a page as a Poisson count averaging 2.5 per page. Four pages are independent. Let $T$ be the total number of typos across the four pages.

What distribution does $T$ follow, and what are its mean and variance?

Accepted Answer

Adding independent Poisson counts gives another Poisson whose rate is the sum of the rates. Four identical pages at rate 2.5 pool to rate 4 	imes 2.5 = 10: T \sim 	ext{Poisson}(10), \qquad \mathbb{E}[T] = 10, \qquad \operatorname{Var}(T) = 10. Standard deviation \sqrt{10} \approx 3.16. This is just superposition with equal rates, which is the same as scaling the observation window by 4. Takeaway. Summing four independent Poisson(2.5) pages gives Poisson(10); mean and variance are both 10.

Total typos across four pages

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