The expected number of trials for achieving two consecutive successes in a Bernoulli experiment with success probability p is given by the formula \(\frac{p+1}{p^2}\). This topic has been extensively analyzed by Mike Spivey, particularly in the context of the probability mass function (pmf) and probability generating function (PGF) for such distributions. Understanding this derivation is crucial for accurately calculating expected outcomes in probabilistic experiments.
PREREQUISITESMathematicians, statisticians, and students studying probability theory, particularly those interested in discrete random variables and their applications in real-world scenarios.