Consider the generalization of the ordinary Poisson process, called the com-pound Poisson process. In an ordinary Poisson process, we assumed that theprobability of occurrence of multiple events in a small interval is negligible withrespect to the length of the interval. If the arrival of a message in a LAN (localarea network) is being modeled, the counting process may represent the num-ber of bytes (or packets) in a message. In this case suppose that the pmf of thenumber of bytes in a message is specified:P[number of bytes in a message = k] = ak, k 1.Further assume that the message-arrivals form an ordinary Poisson process withrate . Then the process {X(t) | t 0}, where X(t) = number of bytes arriving inthe interval (0, t], is a compound Poisson process. Show that generating functionof X(t) is given byGX(t)(z) = et[GA(z)1],whereGA(z) = k1akzk.

Statistics: Intro information Data: What is it o information we collect and organize o facts and figures o numbers and text What is the point of Statistics o To process data so that it is useful o Provide meaningful information in an easily accessible way o Answer questions o Tell a story Help business leaders o Improved insight about operations o Make decisions that are: (prove your opinion is right) Data-driven Fact-based o Not based on speculation o EX: UPS, to increase productivity Benefits of Data and Statistics o Reduce cost o Increase profit