Mathematical Models: Exercise Development
Introduction
In this activity, the probabilistic models used in research are developed in detail, in which, through statistical techniques, statistical inferences are carried out to a conglomerate or population group with intentions to advance to the real facts and through probability, countwith attention plans and programs in each field and discipline in which probabilistic models are used.
It must consider that currently, the use of statistical tools is extremely important for the proper functioning of various areas of human knowledge, in which knowledge is what we know, information or data is the communication of knowledge and thus, the data to applymathematical and probabilistic formulas;The data becomes important information when relevant and basic for decision making to face some specific problems.
And so on, the information becomes a fact when it is backed by data, and ultimately the facts become knowledge when they are implemented in and used properly in decision making with authentic birth of cause and effect, based on a modelProbabilistic.
Developing
Considering that with the implementation of probabilistic models in various areas of science and in the very different disciplines they allow to be used to protect themselves from uncertainty, as well as exploit uncertainty more precisely.
Therefore, we must ensure that probability is important in the decision -making process, in different areas and institutions, as in the same social sciences and even in our daily lives and in which in an imaginary framework, for example, in very fewoccasions there is sufficient information available, thus most decisions are made for uncertainty, which is why the probability acquires great importance.
Probabilistic models are focused on statistical applications for the evaluation of un controlled events, as well as the risk assessment of decision making. We verify that, according to the development of the statistical subject for public security research, three of the most recurrent and used probabilistic models are described in public safety, which are:
Binomial probabilistic model
Which is considered a discrete probability distribution that describes the number of successes when making an unseed number of experiments or repetitions independent of each other, about a variable that could well be random.
Thus, for a variable to be considered binominal, it should comply with characteristics such as:
- In each essay, experiment, etc. Only two probable results are available and that both probabilities can be constant to repeat.
- What a repetition or experiment attempt is independent of the previous one, bone that does not affect the previous result
- That there could not be two simultaneous results in each experiment or test performed
Poisson
Poisson’s distribution is used in a defined situation such as, for example, you want to quantify the number of times or events of a specific type and its occurrence in an established time interval or given space. In short, it refers to the number of events, even infinitely speaking, events could be developed in a time space to consider as planned for the corresponding study.
In the development of the probabilistic model, it should not be neglected that in this type of distribution the number of successes that occur per unit of time is totally at random and in addition each time interval studied is independent of another intervalola general formula forThis distribution is:
Probabilistic model of normal distribution:
It is the most important continuous model of statistics and probability, this for its direct application and in which it will be seen that many relevant variables can be described by said model, as well as its properties;that have allowed in parallel the development of multiple techniques of statistical inference among its main characteristics is that:
- • Many random processes and variables behave in the same way,
- • It is regular use in the approach to other types of probability distributions
- • In samples, related variables and their central tendency measures such as fashion, median, etc. They are practically the same.
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.
Exercise development
For the previous exercise, it should be considered that:
- Determine and indicate what type of distribution can be used.
- For the present case it is binomial
Clearly explain your arguments.
- • That descendants inherit a recessive gene, whatever it is, does not influence that another descendant acquires a recessive gene.
- • There are only two possible answers, contain recessive genes R, R, or not, because the combinations D and D, as well as D and R would be considered similar.
- • Because a parent can inherit genic generic order, according to its generic order, its value to consider is .5, so the event or event can be considered as success or negative.
Write the corresponding model with the appropriate parameters. Assigning values, the probability of creating a pure recessive descend.fifty.5 = 25 %. Of all the possible combinations of descendants D, D, – D, R – R, D – R, R assigning values, we would get a 3/4 3/4 3/4 1/4 = 108/256 = 0.42
Therefore, it would be a 42 % probability according to the equation that a descendant that was not recessive is obtained.
Therefore, the use of statistical models such as the case of binomial distribution results in that it is valuable when making calculations on failures or successes of a particular event. In public safety, the use of this type of distribution studies would allow at a certain time to be able to anticipate the possible bad actions and the results provided, verify the good form of the plans and programs to be developed.
conclusion
Probabilistic models should be visualized in such a way that actions are based on the results that are expected and through the use of statistical techniques for estimation, test and prediction. Thus, it is clear that probabilistic models, the risk means uncertainty for which the probability distribution is known. Thus, the risk assessment is contained in a study to determine the results of the actions with their probabilities.
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