Dear readers of the Fund. First of all apologize for being a bit lost lately, and even more have been so neglected this section. But back to her and with a passionate theme: the laws of probability.
Let's define a few concepts. We had talked about what was a variable, a characteristic of a particular phenomenon. Today we realize a little more.
Imagine a population, such as the population of a country. Now define a set of events, such as hair color that is xi. As everyone will have a certain color hair, there will be a specific frequency for each color, right?
This means that in this population, the total probability is distributed among the different colors (or xi), or what is, hair color has a probability distribution determined for this population. Moreover, this distribution may be typical of that population, for example people in Spain, compared with that of another country, as inhabitants of Sweden. are distinct populations with different probability distributions.
However it may happen that the probability distribution of hair color of a population is the same as that of another population, for example between Sweden and Norway (for instance). That is, both populations follow the same probability distribution.
course we can not go to all the people of a country to look at his hair color. What we do is take a sample , A group of people to look at his hair color, and thus try to understand the distribution of the population. But if we take a sample of the South can give us some different results than if we take in the north (and talk about the bias ). Still, if we get a significant enough sample, we can reach a reasonable approximation of what happens to the population. Conclusion: the true probability distribution is something that almost never know with complete and absolute precision .
Mathematically it is difficult to work with colors instead of numbers, therefore, to work mathematically with the distribution probability (since the statistic is, after all a branch of mathematics) need to introduce another concept random variable. Imagine
other population, the results of successive rolls of a die. In a particular shot can be 6 elementary events, which leaves a 1, a 2, 3 ... and up to 6. A random variable is simply assigned a number to each event, and how easy is that when you get a 1, x = 1, where a 2, x = 2 .... for the six elementary events. But it has to be as simple as that. There are no elementary events, which are compounds. For example comes out even or odd (if is odd and = 1, and if even y = 0). Or if we are interested only 6, the number of times we were out in successive runs (z = number of 6 to go when you roll a die n times). That is, when something happens, give a number (the one you want)
random variables, and variables that are good, can be continuous or discrete, quantitative or qualitative ... For example, in a survey conducted to students in a class, can be very satisfied, satisfied, normal, dissatisfied and not satisfied. A random variable can be very satisfied that we give it a 4 and not satisfied by 0, and the rest of degrees corresponding values. It is a discrete variable can only take certain numbers (no, for example, 4.3456324), qualitative, and that numerically it means nothing, and ordinal, because although the numbers mean nothing, the order itself.
Another example is the random variable length of the tail of cats. Thus, when the tail is 32.5134 cm, x = 32.5134. This is a quantitative continuous variable.
And all you want to invent. It's that simple, one possible event, a numerical value. Let us see how it fit into the probability distribution.
We said that in a probability distribution, each event is assigned a probability. That is, each random variable we give a value between 0 and 1. Or that is, the probability function is function of the random variable. But not all the functions they serve. They can only give positive values, since the probability is never negative, and the total area under the curve is worth 1 (come on, the integral from minus infinity to infinity)
This area is the probability that a value for the variable randomly between the two values \u200b\u200bthat determine the area. Mathematically using an integral, which is a calculation that gives you exactly infinitesimal areas between two extremes.
is called Distribution Function to the function tells you the probability that a value lower x. And this equation is always increasing (because probabilities can only be added) and converges to 1. But hey, this is something quite abstract ...
Another feature is the amount . It tells you the probability that just x, where x is a random variable Discrete . As an example, the dice, the probability that a given value is 1 / 6, so mathematically
f (x) = 1 / 6 when x = 1, 2, 3, 4, 5, 6
f (x) = 0 for other values \u200b\u200bof x
That is a function of size (quite Sencillito).
But continuous variables are a bit pesky, and that the probability of a given event is 0. But how is this possible?: Simple, when continuous, albeit finite, have infinite values \u200b\u200b(between 0 and 1 are infinite numbers, get to play with the decimal ...). As the total probability must be 1, and must be shared among these infinite values \u200b\u200b1 from infinity is 0.
But do not worry because we did not stay with the c *** in the air for continuous we density functions. which gives us a fairly accurate idea of \u200b\u200bwhat may be the probability of a given event.
So you know, all the probabilities of some events we can represent them as functions. And although there are features of many types, nature can be wonderful, but unoriginal, so they always repeat certain functions well studied, which are the Laws of Distribution. The most important: the normal or Gaussian distribution, but there are a few more, and those will be the subject of future entries.
If you have remaining questions, I will be delighted to meet them. Maybe the post has been rougher than I would have liked ... but what follows is more entertaining.
Let's define a few concepts. We had talked about what was a variable, a characteristic of a particular phenomenon. Today we realize a little more.
Imagine a population, such as the population of a country. Now define a set of events, such as hair color that is xi. As everyone will have a certain color hair, there will be a specific frequency for each color, right?
This means that in this population, the total probability is distributed among the different colors (or xi), or what is, hair color has a probability distribution determined for this population. Moreover, this distribution may be typical of that population, for example people in Spain, compared with that of another country, as inhabitants of Sweden. are distinct populations with different probability distributions.
However it may happen that the probability distribution of hair color of a population is the same as that of another population, for example between Sweden and Norway (for instance). That is, both populations follow the same probability distribution.
course we can not go to all the people of a country to look at his hair color. What we do is take a sample , A group of people to look at his hair color, and thus try to understand the distribution of the population. But if we take a sample of the South can give us some different results than if we take in the north (and talk about the bias ). Still, if we get a significant enough sample, we can reach a reasonable approximation of what happens to the population. Conclusion: the true probability distribution is something that almost never know with complete and absolute precision .
Mathematically it is difficult to work with colors instead of numbers, therefore, to work mathematically with the distribution probability (since the statistic is, after all a branch of mathematics) need to introduce another concept random variable. Imagine
other population, the results of successive rolls of a die. In a particular shot can be 6 elementary events, which leaves a 1, a 2, 3 ... and up to 6. A random variable is simply assigned a number to each event, and how easy is that when you get a 1, x = 1, where a 2, x = 2 .... for the six elementary events. But it has to be as simple as that. There are no elementary events, which are compounds. For example comes out even or odd (if is odd and = 1, and if even y = 0). Or if we are interested only 6, the number of times we were out in successive runs (z = number of 6 to go when you roll a die n times). That is, when something happens, give a number (the one you want)
random variables, and variables that are good, can be continuous or discrete, quantitative or qualitative ... For example, in a survey conducted to students in a class, can be very satisfied, satisfied, normal, dissatisfied and not satisfied. A random variable can be very satisfied that we give it a 4 and not satisfied by 0, and the rest of degrees corresponding values. It is a discrete variable can only take certain numbers (no, for example, 4.3456324), qualitative, and that numerically it means nothing, and ordinal, because although the numbers mean nothing, the order itself.
Another example is the random variable length of the tail of cats. Thus, when the tail is 32.5134 cm, x = 32.5134. This is a quantitative continuous variable.
And all you want to invent. It's that simple, one possible event, a numerical value. Let us see how it fit into the probability distribution.
We said that in a probability distribution, each event is assigned a probability. That is, each random variable we give a value between 0 and 1. Or that is, the probability function is function of the random variable. But not all the functions they serve. They can only give positive values, since the probability is never negative, and the total area under the curve is worth 1 (come on, the integral from minus infinity to infinity)
This area is the probability that a value for the variable randomly between the two values \u200b\u200bthat determine the area. Mathematically using an integral, which is a calculation that gives you exactly infinitesimal areas between two extremes.
is called Distribution Function to the function tells you the probability that a value lower x. And this equation is always increasing (because probabilities can only be added) and converges to 1. But hey, this is something quite abstract ...
Another feature is the amount . It tells you the probability that just x, where x is a random variable Discrete . As an example, the dice, the probability that a given value is 1 / 6, so mathematically
f (x) = 1 / 6 when x = 1, 2, 3, 4, 5, 6
f (x) = 0 for other values \u200b\u200bof x
That is a function of size (quite Sencillito).
But continuous variables are a bit pesky, and that the probability of a given event is 0. But how is this possible?: Simple, when continuous, albeit finite, have infinite values \u200b\u200b(between 0 and 1 are infinite numbers, get to play with the decimal ...). As the total probability must be 1, and must be shared among these infinite values \u200b\u200b1 from infinity is 0.
But do not worry because we did not stay with the c *** in the air for continuous we density functions. which gives us a fairly accurate idea of \u200b\u200bwhat may be the probability of a given event.
So you know, all the probabilities of some events we can represent them as functions. And although there are features of many types, nature can be wonderful, but unoriginal, so they always repeat certain functions well studied, which are the Laws of Distribution. The most important: the normal or Gaussian distribution, but there are a few more, and those will be the subject of future entries.
If you have remaining questions, I will be delighted to meet them. Maybe the post has been rougher than I would have liked ... but what follows is more entertaining.
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