What does random mean and what is a random process

Like a lottery ticket, whatever the machine shakes out is the result of heaven.

Random is just a random selection of many items.

There are no rules for selection, and there is a sense of drawing lots.

A stochastic process is a set of parameters that dependRandom variablesThe parameter is usually time. A random variable is a quantitative representation of a random phenomenon, and its value changes with the influence of the accidental dispersion factor.

For example, the number of customers that a store receives in the time from time t0 to time tk is a set of random variables, i.e., random processes, that depend on time t.

The theory of the process of the pre-machine process was born in the early 20th century, and it is based on physics, biology, and management science.

and other aspects of the need for cavity and gradually developed. At present, it has a wide range of applications in automatic control, public utilities, management science, etc.

Development Overview:

Around 1907, . .Markov studied a list of random variables with specific dependencies, which came to be known as Markov chains.

1923 nWiener.

Brownian motion is given.

This process is still an important object of study today. Nevertheless, the study of the general theory of stochastic processes is generally considered to have begun in the 30s.

In 1931, . .Kolmogorov published "Analytical Methods of Probability Theory"; Three years later, . .Sinchin published "The Theory of Stationary Processes". These two important articles are the Markov process.

with a smooth process laid a theoretical foundation. Later, pLévy has published two books on Brownian motion and additive processes, which contain a wealth of probabilistic ideas.

In 1953, Dub's famous book "The Theory of Stochastic Processes".

It systematically and rigorously describes the basic theory of stochastic processes.

In 1951, Ito Kiyoshi established the theory of stochastic differential equations for Brownian motion, which opened up a new way for the study of Markov processes.

Non-deterministic signals are random signals.

Characteristic parameters of random signals:

The main characteristic parameters of the random signal are:

Mean, mean square, variance, probability density function, correlation function, and power spectral density function to describe the properties of stochastic processes.

The power spectrum is an important parameter that describes the basic characteristics of a random signal.

Random signal, a signal whose amplitude is unpredictable but obeys certain statistical characteristics, is also known as an uncertain signal.

The signals transmitted in the general communication system have a certain degree of uncertainty, so they are all random signals, otherwise it is impossible to transmit any new information, and the meaning of communication is lost.

In addition, in the process of signal transmission, it is inevitable to be affected by various interferences and noises, which also have random characteristics and belong to random noise. Random noise is also a type of random signal, but it doesn't carry information. In the calculation of digital filter and fast Fourier transform, due to the limitation of the operation word length, the finite word length effect is generated.

This effect, regardless of whether it is truncated or rounded, produces noise and can be regarded as random noise.

There are many ways to classify signals, and they can be classified from different angles. In signal and system analysis, we often classify buried cavities by the time function characteristics of the signal. In this way, the signal can be divided into definite signal and random signal, continuous time signal and discrete time signal, periodic signal and non-periodic signal, energy signal and power signal, real signal and complex signal, etc.

The 5 common random phenomena in life are as follows:

1. Toss a coin, there may be heads and tails.

2. Throw a dice, there may be a certain one between 1 point and 6 points, as for which one appears first, I don't know in advance.

3. The number of customers entering the supermarket in a day.

4. The market share of a new product in the future.

5. The time when a customer is queuing up in the supermarket to pay.

A random phenomenon is a phenomenon in which there is more than one possible outcome under certain conditions, and it is impossible to know exactly which result will appear in advance, but the results of a large number of repeated experiments have statistical regularity.

Characteristics of random phenomena

Unpredictable phenomena in advance, i.e., repeated experiments under the same conditions, with results that may not be the same each time, or knowing the past state of things, but not being completely certain about future developments.

For example, flipping a coin in the same way may result in heads or tails; When you walk to an intersection, it may be a red light or a green light. Mathematical tools for studying such phenomena are probability theory and statistics.

The common feature of random phenomena and fuzzy phenomena is uncertainty, in random phenomena refers to the uncertainty of the outcome of events, while fuzzy phenomena refer to the uncertainty of the definition of the thing itself. Probability theory and statistics expand the application of mathematics from the field of necessary phenomena to random phenomena, while fuzzy mathematics expands the application of mathematics from the field of clear certainty to the field of fuzzy phenomena.

"Random" is pronounced suíjī, a Chinese word that does not presuppose a position and does not have a specific object.

Source: 1. "Chen Shu Xu Shipu Biography": "The world spectrum is clever, understands the old methods, makes the equipment, and makes random profits and losses, and has wonderful ideas. ”

2. Southern Dynasty Chen Xu Ling "Xiaoyi Temple Tablet": "I wish to give birth to a thousand Buddhas, all of them are sages and saints, although the righteousness of drawing is the same, the sense of randomness is not one." ”

3, Song Chen Liang's "Cui Hao": "And those who don't know the inherent random power of things, Wu can be trivial and worried!" ”

4, the fifteenth chapter of Ming Wu Chengen's "Journey to the West": "If you reach that season when there is no help and no master, you can adapt to the situation and save you from the disaster." ”

5, "The Surprise of the First Moment" volume 31: "You two, only pretend to be family members, when you get there, you must be careful and adaptable." ”

6, Lu Xun "Supplement to the Collection of Extra-Collections" Lying to the Moon": They only thought that they would meet the moon in the future and set off firecrackers to show support, but they didn't expect to meet the tengu as well. And I don't know that even if I don't support it now, if I encounter the moon in the future, I can say something random and perfunctory.

Sentence formation: 1. He has a strong ability to adapt to changes.

2. Be flexible, adaptable, and don't stick to the old rules.

3. This is the time to experience your improvisation.

4. Adaptation is a way of doing things and a kind of wisdom.

5. After this training, you will definitely be amazed at the flexibility of people who are adaptable!

Random, a term used in probability theory. The outcome of something that is often used in everyday life to describe arises from a range of possibilities.

The objective world is in motion, and movement is regular. The laws of material motion can be divided into inevitable laws and statistical laws. The law of necessity refers to the law of the nature of things, which applies to all individuals of things without exception; Statistical law refers to the collective law of things that are presented through a large number of observations of random phenomena.

The laws of statistics are sometimes coincidental and sometimes approximate to the nature of the single individual of things, and sometimes they have nothing to do with each other.

The factors that act on each individual of things in the objective world are divided into two categories: basic factors and secondary factors, the basic factors determine the inevitable laws of things, and the secondary factors make things present statistical laws. The factors that people can recognize and control are the basic factors, and a large number of secondary factors are not recognized or controlled by people, but as long as there are secondary factors, they will inevitably manifest. For example, when launching a cannonball, the basic factor is that people can control its initial conditions -- muzzle velocity, launch angle, etc., which can be calculated through the ballistic equation (inevitable law) to calculate the landing point of the cannonballistic Shenshi branch, but the cannonball will be affected by the resistance of the air during flight - wind speed, wind direction, air humidity, temperature, etc., which makes the cannonball can not fall on its exact destination.

The purpose of scientific research is to discover the objective laws that reflect the essence of things, that is, to eliminate the concealment and interference of contingency, and to do so, we must first understand contingency. Statistics is not a direct study of the inevitable laws of the nature of things, but the discovery of statistical laws of things through random phenomena, and the application of them to the understanding and grasp of objective laws.