Could anyone please suggest on this problem on Poisson Distribution .The problem is that the population in a city is 30000 and that 0.. 1 in each 1000 of the case the accident occurs at random so this is a Poisson Dist. with Lambda = 0.0001*30000=3. One way in which this rate can change is - outbreak M - the occurrence rate of the disease increases to 0.15 for a six month period and then returns to its natural level. To detect this outbreak a notification rule has been devised. For a population of size 30,000 it is :

Report a type M outbreak if the number of occurrences in at least 3 months out of a 6-month period is 5 or more.

what is the probabilty that type M outbreak is reported by the end of a six month period.

Kind Regards,

siddharth

Could anyone please suggest on this problem on Poisson Distribution .The problem is that the population in a city is 30000 and that 0.1 in each 1000 of the case the accident occurs at random so this is a Poisson Dist. with Lambda = 0.0001*30000=3. One way in which this rate can change is - outbreak M - the occurrence rate of the disease increases to 0.15 for a six month period and then returns to its natural level. To detect this outbreak a notification rule has been devised. For a population of size 30,000 it is

Report a type M outbreak if the number of occurrences out of a 6-month period is 5 or more.


what is the probabilty that type M outbreak is reported by the end of a six month period.


Then we want the probability that there are 5 or more outbreaks.

The Poisson distribution is given by \frac{{\lambda}^{x}\cdot e^{-\lambda}}{x!}

But, the problem says 5 OR MORE. Therefore, we find the probabilites for 0 to 4 and subtract from 1.

But, .00015(30000)=4.5={\lambda}

1-\sum_{x=0}^{4}\frac{(4.5)^{x}\cdot e^{-4.5}}{x!}