Johns Hopkins University 3 credits Applied and Computational Mathematics
The Probability and Stochastic Processes I and II course sequence allows the student to more deeply explore and understand probability and stochastic processes. The first course in the sequence provides a deep analysis of fundamental concepts in probability to lay the foundation for the second course, EN.625.722 and other specialized courses in probability. This course builds from previous understanding of probability from Statistical Methods and Data Analysis (EN.625.603) and encourages the student to take a much more critical eye to what a model in probability means and how probability is defined and worked with. The entry point is probability space and random variables. From there, we will consider functions of random variables, along with independence and conditional probabilities. This leads to moments, joint distributions, multivariate random variables, and variance. We then focus more tightly on distributions of random variables, posterior distributions, probability generating functions, moment generating functions, characteristic functions, random sums and the types of convergence and convergence concepts. We cover the law of large numbers and central limit theorems, the Borel-Cantelli Lemmas, order statistics, stable distributions, and extreme value distributions. Our connection point to 625.722 is the last part of the course where we cover homogeneous Poisson processes, non-homogeneous Poisson processes, and compound Poisson processes. This course is proof oriented but will not require measure theory or real analysis. Prerequisite(s): Multivariate calculus and EN.625.603 Statistical Methods and Data Analysis or equivalent
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