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#### Cleopatre VII

##### Guest

I thought that I could share my knowledge of information theory from my studies, starting with probability calculus, which I currently teach in high school and in graduate studies. However, to start the discussion, I would like to write a few introductory posts. I have in mind that not all forum participants deal with mathematics.

This series of posts will focus primarily on information. Today's post is an introduction to the theory of probability. It turns out that the theory of probability and information are related, because the current information theory is based on probability models.

But why does information seem so important? Well, everything we perceive or describe, we get to know precisely because we receive information from the environment. However, we will move on to information itself in further posts.

The basic concept of theory of probability is, of course, the concept of probability itself. Probability may seem to be an intuitive concept, but its mathematical definition requires the establishment of specific models, which, as usually in mathematics, are idealized.

The scientific study of probability is a modern development of mathematics. Gambling shows that there has been an interest in quantifying the ideas of probability for millennia, but exact mathematical descriptions arose much later. There are reasons for the slow development of the mathematics of probability. Whereas games of chance provided the impetus for the mathematical study of probability, fundamental issues are still obscured by the superstitions of gamblers. However, we will talk about them after a short mathematical introduction.

Now let's think about the model of a six-sided dice. Suppose the sides of the dice are indistinguishable, and we can roll a natural number from 1 to 6. In our model the dice is also perfectly symmetrical and no physical conditions are taken into account that may have any influence on the result. Therefore, the discrete probability distribution for a roll of such a dice is as follows:

x_i | 1 | 2 | 3 | 4 | 5 | 6 |

p_i | 1/6 | 1/6 | 1/6 | 1/6 | 1/6 | 1/6 |

x_i - random variables,

p_i - the probability that a random variable has a given value (in this case 1, 2, 3, 4, 5 or 6).

However, to take a closer look at the concept of a random variable, it is worth introducing some mathematical definitions. They will appear in further parts of our discussion.

I kindly ask forum participants to comment on the idea of this discussion and such posts. Do you prefer them to be longer or rather shorter than the current one? How often should they appear?

Let me add that in the next post I would like to discuss the Laplace’s definition of probability.