Chapter 4: Counting and Discrete Probability Models

Learning Objectives

• Define and compute Stirling numbers of the first and second kind
• Relate Bell numbers to set partitions and derive their exponential generating function
• Derive the hypergeometric distribution from sampling without replacement and compare it to the binomial
• State and prove the Poisson limit theorem for the binomial distribution
• Apply Le Cam's inequality to bound the quality of the Poisson approximation
• Model rare events in telecommunications (packet arrivals, interference, massive access) using the Poisson distribution