# Math Help - Poisson Distribuion Problem...

1. ## Poisson Distribuion Problem...

in a certain desert region the number of persons who become seriously ill each year from eating a certain poisonous plant is a random variable having a poisson distribution with 入=5.2. find the probabilities of at least 10 such illnesses in a given year.

2. The Poisson distribution is:
$P(Y=y)=\frac{\lambda^y}{y!}e^{-\lambda}$
The question asks you to find
$P(Y\geq10)$
$P(Y\geq10)=1-P(Y<10)$
$=1-[P(Y=9)+P(Y=8)+P(Y=7)+...+P(Y=0)]$
$=1-\sum_{y=0}^{9}P(Y=y)$