# Basic Concepts of Probability and Statistics

## Abstract

Probability is the measure of chance of occurrence of a particular event. The basic concept of probability is widely used in the field of hydrology and hydroclimatology due to its stochastic nature. The inferences like the expected frequency of events, prediction of hydrologic phenomena based on the dependent variables, risk assessment and modeling require in-depth knowledge of probability theory. This chapter starts with the basic concepts of probability that is required for a clear understanding of random experiment, random variables, events, and assignment of probability to events. The axioms of probability and the fundamental rules are explained with the help of Venn diagrams. Later, the concepts of univariate and bivariate random variables along with their respective forms of probability distribution function, cumulative distribution function, and joint probability distribution are discussed. Application of the probability theories in the field of hydrology and hydroclimatology is illustrated with different examples.