Probability distributions

The negative exponential distribution

The negative exponential distribution is often used 
to model real world events which are relatively rare, such as 
radioactive decay. We have seen that the Poisson distribution 
fits this phenomenun. 



Let's take the example of Iode 131 radioactive decay. If 
N is the number of nuclei at time t = 0. in eight days, it remains 
one half; that is N/2; and in almost six weeks, the Iode 131 sample 
disappear completetely. 


If nj is the number nuclei at the time t nj/N can  represents a 
probability distribution because nj satisfy the following:

0 ≤ nj ≤ N
∑ nj = N