Classroom note: Waiting for a sequence pattern in independent multinomial observations

Abstract

The expected value (mean) is one of the most important measures of central tendency used both in statistics and in the mathematical theory of probability. Using the method of geometric transforms (probability generating functions), the expected number of observations is obtained until the sequence pattern 123…N123…N…123…N, which is an outcome in a sequence of independent multinomial observations. The results and the flow graph analysis obtained agree with and provide the generalization of similar problems considered earlier in this journal.