Probability and random variables

UNIT – I

Chapter - 1

PROBABILITY AND RANDOM VARIABLES

Axioms of Probability - Conditional Probability - Baye's theorem Discrete and continuous random variables Moments Moment generating functions - Binomial, Poisson, Geometric, Uniform, Exponential and Normal distributions - Functions of a random variable.

INTRODUCTION

The theory of probability had its origin in gambling and games of chance. It owes much to the curiosity of gamblers who prestered their friends in the mathematical world with all sorts of questions. Unfortunately, this association with gambling leads to very slow and sporadic growth of probability theory as a mathematical discipline.

The first attempt at some mathematical rigor is credited to Laplace. Laplace gave the classical definition of the probability of an event that can occur only in a finite number of ways as the proportion of the number of favourable outcomes to the total number of all possible outcomes, provided that all the outcomes are equally likely.

Laplace said "We see that the theory of probability is at bottom only common sense reduced to calculation, it makes us appreciate with exactitude what reasonable minds fell by a sort of instinct, often without being able to account for it... It is remarkable that this science, which originated in the consideration of games of chance, should have become the most important object of human knowledge... The most important questions of life are, for the most part, really only problems of probability".