Probability and Statistics: Analyzing Rain Sequences with Bernoulli Trials

Understanding whether daily weather patterns are purely random or depend heavily on the previous day's weather is a fundamental challenge in engineering hydrology and environmental planning. This text-based course guides you through the process of analyzing sequential binary data—such as rainy and non-rainy days—using core probability theory and statistics. You will learn how to model these sequences, evaluate dependencies, and apply these concepts to practical engineering scenarios. What you'll learn: Understand the mathematical foundations of Bernoulli trials and binary sequences; Analyze sequential environmental data to identify statistical dependence; Calculate transition probabilities for binary time series; Apply statistical tests to evaluate if a sequence fits a Bernoulli model; Explore how modern environmental engineers model climate risks using sequential data. The course begins with foundational definitions of probability, independent trials, and the Bernoulli distribution. You will then progress to analyzing binary time series datasets, calculating transition probabilities, and performing statistical tests of independence. Designed for beginners in engineering, environmental science, and data analysis, this course requires only basic algebra and an interest in statistical modeling. Start analyzing environmental data with statistical confidence today.