Max-stable random fields play a central role in modeling extreme value phenomena. We obtain an explicit formula for the conditional probability in general max-linear models, which include a large ...

Branching processes in random environments constitute a significant class of stochastic models designed to capture the interplay between intrinsic reproductive dynamics and extrinsic environmental ...

Part-I, Probability (Chapters 1 – 3), lays a solid groundwork for probability theory, and introduces applications in counting, gambling, reliability, and security. Part-II, Random Variables (Chapters ...

Probability review: probability spaces, axioms of probability, conditional probabilities, independence, random variables, expectation, conditional expectation, inequalities. Limit theorems – laws of ...

Accurate diagnosis of process modes for industrial processes is critical to safe and reliable operation of processes. The hidden Markov models (HMMs) have been widely employed to solve the real-time ...

H. K. ALEXANDER, CONDITIONAL DISTRIBUTIONS AND WAITING TIMES IN MULTITYPE BRANCHING PROCESSES, Advances in Applied Probability, Vol. 45, No. 3 (SEPTEMBER 2013), pp. 692-718 ...

Explain why probability is important to statistics and data science. See the relationship between conditional and independent events in a statistical experiment. Calculate the expectation and variance ...