Answer to Question #257377 in Statistics and Probability for Eugene

Question

On average 3 accidents happens every week in a certain city. What is the probability that we will observe 9 accidents in a month

Answer 1

X ~ Poisson( λ=3)

$P(X=x)= \frac{e^{- λ} λ^x}{x!} \\ P(X=9) = \frac{e^{-3} 3^9}{9!} \\ = \frac{0.04978 \times 19683}{362880} \\ = 0.0027$