Question

Let Xi represent the number of typographical errors on page i of a 500 page book. Suppose that Xi follows a Poisson distribution with parameter lambda=0.1, independently for each page. Determine the probability that a randomly selected page contains at least one typographical error.

Answer 1

\(X\sim\text{Poisson}(\lambda=0.1)\), so you need to know \(P(X \ge 1)\). Since the support of the Poisson random variable starts at x=0, it is easy to find the complement, that is \(P(X\ge 1)=1-P(X<1)=1-P(X=0)\)

where, of course, \(P(X=x)=\dfrac{e^{-\lambda}\lambda^x}{x!}\)

Answer 2

Oh, okay. So just plug in lambda and x=0 in the Poisson pdf?

Answer 3

yes, pretty much, just don't forget the 1 - part :)

Answer 4

alright, thank you :)

Answer 5

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