Bienvenida y comentarios acerca de la creacion del blog

Este blog fue creado con la intención de ofrecer la información, formulas, métodos,  y análisis de los temas tratados para la solución de los ejercicios planteados aquí mismo. 

Durante su creación se presentaron algunas dificultades que impedían proseguir, por ejemplo el desconocimiento o la complejidad de desarrollar algún subtema y resolver los ejercicios propuestos, aunque cabe señalar que gracias a la consulta de algunos libros que ofrece la institución mismos que se encuentran señalados en el apartado bibliográfico, ademas de la consulta al asesor de la materia se logro satisfactoriamente el objetivo.

También es importante dar agradecimiento a los dueños de los canales de Youtube de los cuales fueron tomados algunos vídeos explicativos de ejercicios.

Como conclusión final resaltar la clara diferencia de aprendizaje y conocimiento (sobretodo por parte de los autores ) entre el antes de empezar y al final al presentar el blog, donde la mayoría mostraron cierto dominio sobre el tema y se logro una buena experiencia.

Clarifications about the English version

From this post the same content of the blog is offered in the English language, this with the purpose of expanding the coverage of it and offering more students or common people the information presented here, adapting completely even the images, and only omitting the videos presented


Enjoy the content in English, and in case you find any error in the translation do not hesitate to leave the comment to correct the error as soon as possible and improve the content

5.1.7 Measurement errors



The measurement error is defined as the difference between the measured value and the "true value". Measurement errors affect any measuring instrument and can be due to different causes. Those that can be predicted in some way, calculated, eliminated by calibrations and compensations, are called deterministic or systematic and are related to the accuracy of the measurements. Those that can not be predicted, because they depend on unknown causes, or stochastic, are called random and are related to the precision of the instrument.

Random error The laws or mechanisms that cause it due to its excessive complexity or its small influence on the final result are not known.

To know this type of errors we must first make a sampling of measurements. With the data of the successive measurements we can calculate its mean and sample standard deviation.

Systematic error They remain constant in absolute value and in the sign when measuring, a magnitude in the same conditions, and the laws that cause it are known.

To determine the systematic error of the measurement, a series of measurements must be made on a quantity Xo, the arithmetic mean of these measurements must be calculated and then the difference between the mean and the magnitude X0 must be found.

Systematic error = | media - X0 |

Although it is impossible to know all the causes of the error, it is convenient to know all the important causes and have an idea that allows us to evaluate the most frequent errors. The main causes that produce errors can be classified as:

Error due to the measuring instrument.
Error due to the operator.
Error due to environmental factors.
Error due to geometric tolerances of the piece itself.

5.1.6 Confidence intervals and tests for the correlation coefficient

5.1.6 Confidence intervals and tests for the correlation coefficient

In statistics, it is called confidence interval to a pair or several pairs of numbers between which it is estimated that there will be a certain unknown value with a certain probability of success. Formally, these numbers determine a range, which is calculated from data from a sample, and the unknown value is a population parameter.

The probability of success in the estimation is represented by 1 - α and is called confidence level. In these circumstances, α is the so-called random error or level of significance, that is, a measure of the possibilities of failure in the estimation by such an interval.

Use the confidence interval to evaluate the estimation of the population parameter. For example, a manufacturer wants to know if the average length of the pencils he produces is different from the target length. The manufacturer takes a random sample of pencils and determines that the average length of the sample is 52 millimeters and the confidence interval of 95% is (50.54). Therefore, you can be 95% sure that the average length of all pencils is between 50 and 54 millimeters.

5.1.5 Two-dimensional normal distribution

5.1.5 Two-dimensional normal distribution


In statistics, the binomial distribution is a discrete probability distribution that counts the number of successes in a sequence of n independent Bernoulli trials, with a fixed probability p of occurrence of success between trials.

A Bernoulli experiment is characterized by being dichotomous, that is, only two results are possible. One of these is called "success" and has a probability of occurrence p and the other, "failure", with a probability q = 1 - p. In the binomial distribution, the experiment is repeated n times, independently, and the probability of a certain number of successes is calculated.

To represent that a random variable X follows a binomial distribution of parameters n and p, it is written:


                                                             





Its probability function is




where 

5.1.4 Linear correlation coefficient

5.1.4 Linear correlation coefficient



The linear correlation coefficient is the quotient between the covariance and the product of the standard deviations of both variables.

Properties
1.
The correlation coefficient does not change when the measurement scale does it.
That is, if we express the height in meters or in centimeters, the correlation coefficient does not change.

2.
The sign of the correlation coefficient is the same as that of the covariance.

3.
  The linear correlation coefficient is a real number between -1 and 1.

Four.
  If the linear correlation coefficient takes values close to -1, the correlation is strong and inverse, and will be stronger the closer a r approaches -1.

5.
  If the linear correlation coefficient takes values close to 1, the correlation is strong and direct, and will be stronger the closer a r approaches.

6
  If the linear correlation coefficient takes values close to 0, the correlation is weak.

7
  If r = 1 or -1, the points of the cloud are on the increasing or decreasing line. Between both variables there is functional dependence.

5.1.3 Correlation

5.1.3 Correlation



By definition, the correlation is the correspondence or relationship between two or more things, in statistics, the degree of dependence between random variables that intervene in a multidimensional distribution. It is that which indicates the force and the linear direction that is established between two random variables.


It is considered that two variables of a quantitative type have a correlation with each other when the values of one of them vary systematically with respect to the homonymous values of the other. For example, if we have two variables that are called A and B, there will be the aforementioned correlation phenomenon if increasing the values of A are also the values of B and vice versa