Answer to Question #171044 in Statistics and Probability for Shiv Om

Question #171044

In a town 10 accidents took place in a period of 50 days. Assume that the number of accidents per day follow Poisson distribution. Find the probability that there will be three or more accidents per day.


1
Expert's answer
2021-03-15T08:03:12-0400

For random variable from Poisson distribution with parameter λ\lambda :

λ=EX=1050=0.2\lambda = EX = \frac{10}{50} = 0.2 , where EXEX is sample mean

Distribution function:

Pr(X=k)=eλλkk!=e0.20.2kk!Pr(X=k) = e^{-\lambda}\frac{\lambda^k}{k!} = e^{-0.2}\frac{0.2^k}{k!}

Hence,

Pr(X3)=1Pr(X<3)=1k=02Pr(X=k)=1e0.2(1+0.21+0.222)=0.0011Pr(X \geq 3) = 1 - Pr(X < 3) = 1 - \sum_{k=0}^{2}Pr(X=k) = 1 - e^{-0.2}(1 + \frac{0.2}{1} + \frac{0.2^2}{2}) = 0.0011

So, the probability is approximately 0.11%



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