An Inventory Model - A hot dog vendor operates a stand where the number of hot dogs he sells each day is modeled as a Poisson random variable with a mean value of 100.

Let represent the number of hot dogs the vendor has at the beginning of each day.

At the end of the day, if his inventory of hot dogs on hand falls below some minimum value, α , then the vendor goes out that evening and purchses enough hot dogs to bring the total of his inventory to ß Write an equation to describe the elements of the transition probability matrix, pi j for this inventory process.