TRAFFIC MODELS MPEG2 (sport) Voice Data MPEG2 (news) Poisson
Distribution Poisson process Discrete events in an interval The
probability of one success in an interval is stable The probability
of more than one success in this interval is 0 The probability of
success is independent from interval to interval e.g.: The number
of customers arriving in 15 minutes PXx x x (| ! e - e.g.: Find the
probability of four customers arriving in three minutes when the
mean is 3.6. Poisson Distribution Formula where: X = number of
successes per time period = expected number of successes per time
period e = base of the natural logarithm system ( ) Graph of
Poisson Probabilities X = P(X = 2) =.0758 Graphically: =.50 Poisson
Distribution Shape The shape of the Poisson Distribution depends on
the parameter : = 0.50 = 3.00 In-Class Exercises: 1a. If calls to
your cell phone are a Poisson process with a constant rate =2 calls
per hour, whats the probability that, if you forget to turn your
phone off in a 1.5 hour movie, your phone rings during that time?
1b. How many phone calls do you expect to get during the movie?
Answer 1a. If calls to your cell phone are a Poisson process with a
constant rate =2 calls per hour, whats the probability that, if you
forget to turn your phone off in a 1.5 hour movie, your phone rings
during that time? X ~ Poisson ( =2 calls/hour) P(X1)=1 P(X=0)
P(X1)=1 .05 = 95% chance 1b. How many phone calls do you expect to
get during the movie? E(X) = t = 2(1.5) = 3
