<P> This equation is the probability mass function (PMF) for a Poisson distribution . </P> <P> On a particular river, overflow floods occur once every 100 years on average . Calculate the probability of k = 0, 1, 2, 3, 4, 5, or 6 overflow floods in a 100 - year interval, assuming the Poisson model is appropriate . </P> <P> Because the average event rate is one overflow flood per 100 years, λ = 1 </P> <Dl> <Dd> P (k overflow floods in 100 years) = λ k e − λ k! = 1 k e − 1 k! (\ displaystyle P (k (\ text (overflow floods in 100 years))) = (\ frac (\ lambda ^ (k) e ^ (- \ lambda)) (k!)) = (\ frac (1 ^ (k) e ^ (- 1)) (k!))) </Dd> </Dl>

Explain poisson distribution with their properties and uses