Understand and know the mathematical models
Introduction
In this unit corresponding to this subject, we will study the different probabilistic models, analyzing the characteristics of each of them, and know the similarities that exist between them. The probabilistic models that we will analyze will be;Binomial, Poisson and Normal. I will begin by describing that it is a probabilistic model, it is a mathematical model that uses probability, the result of a data generated data set, so that the data of a larger population resembles, the resulting hypotheses describe a set of distributionsof probability, which are capable of approaching that data set with that of the total population.
Developing
Sample, it is a subset taken from a population, it is a small amount of cases, or individuals that are considered representative of a total, which is taken from that population, and with it the methods will be used for study, analysis or experimentation and be able to achieveConclusions applicable to the total population from which the sample was extracted, in public safety you can take the number of robberies house room in Mexico and work looking for days, places or sites with greater incidence and from there to establish to establish a program or public policy.
Population, in statistics it is a term used to name the set of reference elements on which observations are made, it is also called collective universe. Probabilistic or statistical data, a probabilistic model of an experiment requires associating an likelymathematician that uses the probability that includes a set of assumptions on the generation of some sample data, in such a way that they resemble data from a larger population.
It is important to mention that there are probabilistic models for both discrete and continuous variables. A statistical model is specified by a set of equations that relate various random variables, so a model is a formal representation of a theory ’, statistical models are a fundamentally part of statistical inference.
Binomial: a binomial distribution is a discreet probability distribution that describes the number of successes when performing independent experiments on a random variable. For a random variable to be considered that it is a binomial distribution, it has the following characteristics:
- In each experiment only two results are possible.
- The probability of success will be constant, it is represented by letter "P"
- The probability of failure will also be constant, it is represented by the letter "Q" = 1 – P.
- The result obtained in each experiment is independent of the previous one, that is, what happens in each experiment does not affect the following.
- The events cannot occur twice at the same time.
- The random variable that follows a binomial distribution is usually represented as
X ~ (n, p). n represents the number of experiments and p The probability of success.
- The random variable X is defined as the number of successes within a fixed number of trials.
The formula for calculating the normal distribution is:
Where:
n = number of trials/experiments
x = number of successes
P = probability of success
Q = Probability of failure (1-P)
Poisson: It is one of the most important distributions of discrete variable. Its main applications refer to the modeling of situations in which we are interested. Another of its frequent uses is the limit consideration of repeated dichotomous processes a large number of times if the probability of obtaining a success is very small. Within its characteristics of this model we have:
- The realization of certain facts is observed for a certain period of time or along an observation space
- The facts to be observed have random nature;They can occur or not in a non -deterministic way.
- The probability that an X number is produced in an interval of amplitude T does not depend on the origin of the interval (although, on its amplitude)
- The probability of a fact in an infinitésimo interval is practically proportional to the amplitude of the interval.
- The probability that there are 2 or more facts in an infinitésimo interval is an infinitésimo of order greater than two.
- Normal: normal distribution is the most important of all probability distributions, since it is a continuous variable and known for the amount of phenomena it explains.
Within its characteristics we have to:
- Its application is direct and allows you to observe many interest variables, which can be easily described with this model.
- It serves to approach several discrete probability distributions, among these the distribution of Poisson and the binomial distribution.
- Its properties have allowed the development of many statistical inference techniques. Providing the basis of classical inferential statistics, for its relationship with the central limit theorem.
Exercise
Assume that a certain eye color feature, being left -handed, etc. It is determined by a couple of genes, and which also represents a dominant gene, and r a recessive gene. A public security officer with a couple of genes D, d is said to be pure dominant and with the gene couple R, r it is said that it is pure recessive and with a couple d, r is said to be hybrid. Apparently, pure dominant and hybrids are similar. The descendants of a couple receive a gene from each parent and this gene can, with the same probability, be one of the two that the aforementioned parent has.
conclusion
In conclusion to this activity we have to know and perfectly understand these types of models will help us a lot, since through these probabilistic models we can make decisions about events that are studied and at the same time, we can have the evidence to supportSuch decisions, we also understand that they are important because they help us predict the behavior of future repetitions of some random experiment and thus have the opportunity to take the relevant measures to avoid it
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