split - variable expression

mdias

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Jul 2, 2010
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in one town a number of burgualaries in a week has a poisson distribution with a mean of 4.6 find the probobility that in a randomly selected week the number of burglaries is at least 3??
 
The Poisson is given by

\(\displaystyle \frac{{\lambda}^{x}\cdot e^{-\lambda}}{x!}\)

Now, since it says "at least 3", the best thing to do is find the probabilities from 0 to 2 and subtract from 1.

\(\displaystyle 1-\sum_{x=0}^{2}\frac{(4.6)^{x}\cdot e^{-4.6}}{x!}\)

Intuitively, we know that the probability is going to be fairly high, since the average is 4.6 and they are asking for 3 and up.
 
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