## PROBABILITY AND STATISTICS

### PROBABILITY AND STATISTICS INTRODUCTION

A probability distribution is defined in terms of an underlying sample space, which is the set of all possible outcomes of the observed random phenomenon. The sample space can be the set of real numbers or a vector space of a higher dimension, or it can be a list of non-numerical values.

Probability distributions are generally divided into two classes.

A discrete probability distribution (applicable to scenarios where the set of possible outcomes is discrete, such as a coin toss or a dice roll) can be coded by a discrete list of the probabilities of the results, known as the probability mass function . On the other hand, a continuous probability distribution (applicable to scenarios where the set of possible outcomes can take values in a continuous range (for example, real numbers), such as temperature on a given day)

It is typically described by density functions of probability (with the probability that any individual result is really 0. More complex experiments, such as those involving stochastic processes defined in continuous time, may require the use of more general probability measures.

A probability distribution whose sample space is the set of real numbers is called univariate, while a distribution whose sample space is a vector space is called multivariable. A univariate distribution gives the probabilities that a single random variable takes several alternative values;

A multivariate distribution (a joint probability distribution) gives the probabilities of a random vector (a list of two or more random variables) that assume various combinations of values. The important and commonly encountered univariate probability distributions include the binomial distribution, the hypergeometric distribution, and the normal distribution. The multivariate normal distribution is a common multivariate distribution.