Authors of paper describe a data packet switch that uses the statistical behavior of packet arrivals to reduce interconnected complexity. The binomial distribution is used to model the number of packets, out of n, that arrive at any output of the system. Suppose that 16 packets are in the system and the probability of any one packet's arriving an output X is p= 0.15.
a) What is the probability that exactly 2 of the packets arrive at an output?
b) What is the probability that at least 2 of the packets arrive at an output?
c) What is the probability that no more than 1 packet arrives at an output?
d) What is the expected number of packets arriving at an output?
e) What is the standard deviation of the number of packets arriving at an output?
f) What would the answers to a-e be if the probability of any one packet arriving at an output is 0.10?