The Number of Two Consecutive Successes in a Hoppe-Pólya Urn
Lars K. Holst · Journal of Applied Probability · 2008
In a sequence of independent Bernoulli trials the probability of success in the kth trial is pk = a / (a + b + k − 1). An explicit formula for the binomial moments of the number of two consecutive successes in the first n trials is obtained and some consequences of it are derived.