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Markov’s inequality is a helpful result in probability that gives information about a probability distribution. The remarkable aspect about it is that the inequality holds for any distribution with positive values, no matter what other features that it has. Markov’s inequality gives an upper bound for the percent of the distribution that is above aContinue reading “The Markov inequality”

Avarages is a single number that represents the middle value of all the numbers in a list or set. There are 3 different types of average. These are called the mean, the median and the mode. Each one gives slightly different information. MeanThe mean is a type of average. It is the total sum ofContinue reading “The various types of averages: arithmetic, geometric, harmonic, weight, quadratic”

The Weak Law of Large Numbers, also known as Bernoulli’s theorem, states that if you have a sample ofindependent and identically distributed random variables, as the sample size grows larger, the sample mean will tend toward the population mean. More formally, the central limit theorem can be defined as follows: for the sample size→∞ theContinue reading “The weak law of large numbers”

In probability theory, Chebyshev’s inequality guarantees that, for a wide class of probability distributions, no more than a certain fraction of values can be more than a certain distance from the mean. Specifically, no more than 1/k2 of the distribution’s values can be more than k standard deviations away from the mean. The inequality hasContinue reading “Chebyshev inequality”

In the study of probability theory, the central limit theorem (CLT) states that the distribution of sample means approximates a normal distribution (also known as a “bell curve”), as the sample size becomes larger, assuming that all samples are identical in size, and regardless of the population distribution shape.Said another way, CLT is a statisticalContinue reading “The central limit theorem”

The Box–Muller transform is a method for generating pairs of independent, standard, normally distributed random numbers, given a source of uniformly distributed random numbers. The Box–Muller transform is commonly expressed in two forms. The basic form takes two samples from the uniform distribution on the interval [0, 1] and maps them to two standard, normallyContinue reading “Box Muller Transform”

Statistical inference (or inferential statistics) is the procedure by which the characteristics of a population are induced by the observation of a part of it (called “sample”), usually selected through a random (random) experiment. From a philosophical point of view, these are mathematical techniques to quantify the learning process through experience. We will mainly considerContinue reading “Bayes Theorem in statistical inference: the concept of prior, posterior probabilities and the likelihood”

A Data set is obtained through the observation of variables or attributes for a population statistical. Definitions: Statistical unit: object of data collection for which the information is collected. Population Statistical: object of survey, is a set of statistical units from which information is collected. Attribute (or variable): is the property or parameter of theContinue reading “Data set obtained by a population of statistical units and a set of variables”

The statistics is a science that allows to collect, process, analyze and describe datas with the aim of describing them clearly and concisely. The statistics relative to a single variable is called univariate, relative to a set of data is called multivariate. There are two types of statistics: • Descriptive Statistics is used to describeContinue reading “What is Statistics?”