Probability theory forms the mathematical backbone for quantifying uncertainty and random events, providing a rigorous language with which to describe both everyday phenomena and complex scientific ...

In a number of situations we are faced with the problem of determining efficient estimates of the mean and variance of a distribution specified by (i) a non-zero probability that the variable assumes ...

The relative frequency definition of probability says: If an experiment is repeated, the probability of an event (a specified outcome of the experiment) is the relative frequency of occurrence of that ...

Introduction to probability, random processes and basic statistical methods to address the random nature of signals and systems that engineers analyze, characterize and apply in their designs. It ...

This note suggests that expressing a distribution function as a mixture of suitably chosen distribution functions leads to improved methods for generating random variables in a computer. The idea is ...

Sample space, Field and Probability Measure. Axiomatic definition of Probability. Bayes' theorem. Repeated trials. Continuous and discrete random variables and their probability distribution and ...

The world is full of uncertainty: accidents, storms, unruly financial markets, noisy communications. The world is also full of data. Probabilistic modeling and the related field of statistical ...