Machine Learning and Big Data

2Theory of Probability

Parvaze Ahmad Dar and Afroz*

Department of Mathematics, Maulana Azad National Urdu University, Hyderabad, India

Abstract

This chapter is dealing with the theory of probability and its basic and higher concepts like probability, sample space, trial, event, null event, exhaustive events, mutually exclusive events, equally likely events, sure event permutation, and combination, etc. Later on, the Concept of Independence in Probability and Conditional in Probability are discussed. By conditional probability, the occurrence of first event is to expect the probability of second event, this process of reversing such probabilities is known as Baye’s theorem. Finally, we conclude this chapter with the concept of Multivariate Gaussian Function.

Keywords: Event, mutually exclusive events, sample space, independent even, conditional probability, cumulative distribution, Baye’s theorem, multivariate gaussian function

2.1 Introduction

In simple words, “Probability or Chance” state indirectly that its ambiguity about the occurrence of any event. For example, after tossing unbiased coin, the outcome may be head or tail, i.e., there is equal chance or probability of each. The origin of the probability theory is in the games of chance, which is connected to betting like drawing of cards and throwing of a die [1–4].

2.1.1 Definition

2.1.1.1 Statistical Definition of Probability

“Among n trails, an occurrence of the event E happened m times; thus, the probability of happening ...