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.
PROBABILITY AND STATISTICS MATERIAL
