Possion Distribution

• Probability that an event occurs k times within a given time interval
• Eg:
• k meteors within 100 years
• k calls in an hour
• Also can count spatially circumscribed events
• no of dust particles in a mm of air
• no of diamons in ton of ore
• Expected no of events $E[X]$ : rate $\lambda$
• PMF : $p(k)=\frac{{\lambda }^k{e}^{-k}}{k!}$
• 
• Eg:
• N 1-hour protocols for calls : $n_i(i=1,\dots ,N)$
• $\hat{\lambda }=\frac{1}{N}{\Sigma }_i{n}_i$