In many complex systems, randomness plays an integral part in the outcome of an event.
The likelihood of a system to produce an event is based on the initial state and a range of parameters. Results are predicted and described by a number of mathematical methods in this academic field, including: axioms of probability, probability trees, random variables, distributions, conditioning, expectation, change of variables, and limit theorems, discrete and continuous time parameter Markov chains, queuing theory, inventory theory and simulation.