ABSTRACT
This chapter provides the basic knowledge concerning probability theory and statistical inference, from the frequentist and the Bayesian point of views. The chapter examines the foundations of the probability theory, focusing on the definitions of some basic concepts, such as random experiment, sample space, event, and probability. It focuses on the concept of random variable. Probability theory is an abstract mathematical subject, which is built on some basic concepts, such as random experiment, sample space, and event. A Random experiment is any activity whose outcome cannot be predicted with certainty. The classical definition of probability is affected by several weaknesses. In many contexts it is useful to deal with probabilistic models that provide an analytic description of the stochastic nature of a certain phenomenon of our interest. Statistical theory distinguishes according to the availability of observations on the whole population of interest or only on a sample.
