The system of random numbers. Generator random numbers Excel in data functions and analysis
- Tutorial
Have you ever wondered how Math.Random works works? What is a random number and how does it work? And imagine a question on the interview - write your generator of random numbers into a pair of code lines. And so what is it, chance and is it possible to predict it?
I am very fascinated by various IT puzzles and challenges and generator of random numbers - one of these tasks. Usually in your telegrams, I deal with all sorts of puzzles and different tasks from interviews. The task about the random number generator gained great popularity and I wanted to perpetuate it in the depths of one of the authoritative sources of information - then you mean here, on Habré.
This material will be useful to all those frontenderators and Node.js to developers who are on the tip of technology and want to get into the blockchain project / startup, where questions about security and cryptography, at least at the base level, are asked even from the fronters.
Pseudo-random number generator and random number generator
In order to get something random, we need a source of entropy, a source of some chaos from which we will use to generate chance.This source is used to accumulate entropy with the subsequent receipt of the initial value (initial value, seed) from it, which is necessary for generators of random numbers (HSH) to form random numbers.
The pseudo-random number generator uses the only initial value, from where it follows its pseudociality, while the random number generator always forms a random number, having an at the beginning of a high-quality random amount that is taken from various sources of entropy.
Entropy is a mess of disorder. Information entropy is a measure of uncertainty or unpredictability of information.It turns out that to create a pseudo-random sequence we need an algorithm that will generate some sequence based on a certain formula. But such a sequence can be predicted. However, let's fantasize how you could write your generator of random numbers, if we had no math.random ()
GPSH has some algorithm that can be reproduced.
HSH is the receipt of numbers completely from any noise, the ability to calculate that tends to zero. At the same time, there are certain algorithms in the GSH to align the distribution.
We come up with your GPSH algorithm
The pseudo-random number generator (GPSH, English Pseudorandom Number Generator, PRNG) is an algorithm that generates the sequence of numbers, the elements of which are almost independent of each other and are subject to a given distribution (usually uniform).We can take the sequence of some numbers and take the module from them. The easiest example that comes to mind. We need to think what sequence to take the module from what. If simply in the forehead from 0 to N and the module 2, then the 1 and 0 generator will be obtained:
Function * Rand () (Const n \u003d 100; const mod \u003d 2; let i \u003d 0; while (true) (yield i% mod; if (i ++\u003e n) i \u003d 0;)) let i \u003d 0; For (Let X of Rand ()) (IF (I ++\u003e 100) Break; Console.log (x);)
This feature generates us sequence 01010101010101 ... and it is impossible to call it even a pseudo-random one. So that the generator is random, it should take the next bit test. But we do not have such a task. Nevertheless, even without any tests, we can predict the following sequence, which means such an algorithm in the forehead is not suitable, but we are in the right direction.
And what if you take some kind of known, but nonlinear sequence, for example, the number Pi. And as a value for the module, we will take not 2, but something else. You can even think about the topic of the changing value of the module. The sequence of numbers among PI is considered random. The generator can work using the pi numbers, starting at some unknown point. An example of such an algorithm, with a PI base sequence and a variable module:
Const vector \u003d [... math.pi.tofixed (48) .replace (".", "")]; Function * Rand () (for (LET i \u003d 3; I<1000; i++) {
if (i > 99) i \u003d 2; For (Let n \u003d 0; n
We received a number generator from 0 to 9, but the distribution is very uneven and every time it will generate the same sequence.
We can take a number of PI, and time in a numeric representation and this number is considered as a sequence of numbers, and in order for each time the sequence does not repeat, we will read it from the end. Total our algorithm of our GPSH will look like this:
Function * Rand () (Let NewNumvector \u003d () \u003d\u003e [... (+ New Date) + ""]. Reverse (); let vector \u003d newnumvector (); let i \u003d 2; While (true) (if (if ( i ++\u003e 99) i \u003d 2; let n \u003d -1; while (++ n< vector.length) yield (vector[n] % i);
vector = newNumVector();
}
}
// TEST:
let i = 0;
for (let x of rand()) {
if (i++ > 100) Break; Console.log (X))
This is already similar to the pseudo-random number generator. And the same math.random () is a GPSh, we will talk about it a little later. At the same time, each time the first number is obtained different.
Actually, these ordinary examples can be understood as more complex random number generators work. And there are even ready-made algorithms. For example, we will analyze one of them - this is a linear congruent GPP (LCPRNG).
Linear congruent GPSH
Linear Congrunt GPSh (LCPRNG) is a common method for generating pseudo-random numbers. It does not have cryptographic resistance. This method is to calculate the members of the linear recurrent sequence according to the module of some natural number M as defined by the formula. The resulting sequence depends on the choice of the starting number - i.e. seed. With different values \u200b\u200bof SEED, various sequences of random numbers are obtained. An example of this algorithm for JavaScript:Const a \u003d 45; Const C \u003d 21; const m \u003d 67; var seed \u003d 2; const Rand \u003d () \u003d\u003e SEED \u003d (A * SEED + C)% m; for (Let i \u003d 0; i<30; i++)
console.log(rand())
Many programming languages \u200b\u200buse LCPRNG (but not exactly such an algorithm (!)).
As mentioned above, such a sequence can be predicted. So why do we need a GPSh? If we talk about security, the GPSF is a problem. If we talk about other tasks, then these properties can play plus. For example, for various specialistic effects and animations, the graphics may need a frequent RANDOM call. And here the distribution of values \u200b\u200band performances are important! Surveral algorithms can not boast the speed of work.
Another property is reproducibility. Some implementations allow you to set SEED, and it is very useful if the sequence should be repeated. Playback is needed in tests, for example. And many more other things exist, for which the safe GSH does not need.
How Math.Random () is arranged
MATH.RANDOM () method Returns a pseudo-random number of floating semicolons from the range \u003d Crypto.GetRandomValues \u200b\u200b(New Uint8Array (1)); Console.log (RVALUE)
But, unlike GPSh Math.Random (), this method is very resource-intensive. The fact is that this generator uses system calls to the OS to access the sources of entropy (MAK address, CPU, temperature, etc ...).The herorator of random numbers for lottery tickets is provided free of charge in the format "As is" ("As IS"). The developer does not bear any responsibility for the material and intangible loss of script users. You can use this service at your own risk. However, what, and the risk you do not take exactly :-).
Random numbers for lottery tickets online
This software (GPSF on the JS) is a pseudo-random number generator implemented by JavaScript programming language capabilities. The generator issues a uniform distribution of random numbers.
This allows you to knock out the Wedge Wedge on the HSH with a uniform distribution from the lottery company to respond random numbers with a uniform distribution. This approach eliminates the player's subjectivity, since people have certain preferences in choosing numbers and numbers (the birthdays of relatives, memorable dates, years, etc.), which affect the selection of numbers manually.
Free tool helps players pick up random numbers for lotteries. In the random generator script, there is a set of pre-confined modes for Gosloto 5 of 36, 6 of 45, 7 of 49, 4 of 20, Sportlio 6 of 49. You can select the generation mode of random numbers with free settings for other lottery options.
Forecasts Winning Lottery
The random number generator with a uniform distribution can serve as a horoscope on the lottery draw, however, the likelihood that the forecast will be raised by the low. But still, the use of a random number generator has a good probability of winning compared to many other lottery game strategies and additionally frees you from the mucke of a complex choice of happy numbers and combinations. For our part, I do not advise you to succumb to the temptation and buy paid predictions, it is better to spend this money on the textbook on the combinatorics. From it you can learn a lot of interesting things, for example, the probability of winning Jack-Pota in Gosloto 5 of 36 Sociorates 1 to 376 992 . And the probability of getting a minimum prize, guessing 2 numbers, is 1 to 8 . The same probabilities of the winnings have a forecast based on our GSH.
On the Internet there are requests for random numbers for the lottery, taking into account past editions. But provided that the Lottery uses the HSH with a uniform distribution and the probability of falling out of a particular combination does not depend on the circulation to the circulation, then trying to take into account the results of past erases meaningless. And this is quite logical, as the lottery companies are not beneficial for participants to increase the likelihood of their winning simple methods.
There are often conversations that the organizers of the lotteries are fascinated by the results. But in fact, there is no point in this, even, on the contrary, if the lottery companies had influenced the lottery results, it would be possible to find a winning strategy, but until it was possible to anyone. Therefore, the arrangers of lotteries are just very profitable that the balls fall out with a uniform probability. By the way, the estimated return of the lottery 5 of 36 is 34.7%. Thus, a lottery company remains 65.3% of revenue from the sale of tickets, some of the funds (usually half) is deducted to the formation of Jack Pot, the rest of the money goes to organizational expenses, advertising and net profit of the company. Statistics on the resources These numbers perfectly confirms.
Hence the conclusion - do not buy meaningless forecasts, use the free generator of random numbers, take care of your nerves. Let our random numbers become happy numbers for you. Good mood and a good day!
We have a sequence of numbers consisting of practically independent elements that are subject to the specified distribution. As a rule, uniform distribution.
Generate random numbers in Excel can be different paths and ways. Consider only better of them.
Random number function in Excel
- The adhesive function returns a random uniformly distributed real number. It will be less than 1, more than or equal to 0.
- Function The permanent returns a random integer.
Consider their use on examples.
Sampling random numbers using adhesi
This function of arguments does not require (adhesive ()).
To generate a random real number in the range from 1 to 5, for example, we apply the following formula: \u003d adhesive () * (5-1) +1.
Return random number is distributed evenly on the interval.
Each time the sheet is calculated or when the value changes, a new random number is returned in any sheet. If you need to maintain the generated set, you can replace the formula to its value.
- Click on a cell with a random number.
- In the string of formulas, we allocate the formula.
- Press F9. And input.
We check the uniform distribution of random numbers from the first sample using the distribution histogram.
Range of vertical values \u200b\u200b- frequency. Horizontal - "Pockets".
Function rational
The syntax of the function is rational - (lower limit; upper bound). The first argument should be less than the second. Otherwise, the function will give an error. It is assumed that the boundaries are integers. The fractional part of the formula is discarded.
An example of using the function:
Random numbers with an accuracy of 0.1 and 0.01:
How to make a random number generator in Excel
We will make a random number generator with a value generation from a specific range. Use the formula of the form: \u003d index (A1: A10; integer (adhesive () * 10) +1).
We will make a random number generator in the range from 0 to 100 in increments of 10.
From the list of text values \u200b\u200byou need to select 2 random. Using the adrision function, we compare text values \u200b\u200bin the A1 range: A7 with random numbers.
We use the function as an index to select two random text values \u200b\u200bfrom the source list.
To select one random value from the list, apply such a formula: \u003d index (A1: A7; rationing (1; account (A1: A7))).
Generator of random numbers of normal distribution
Functional features and permanent random numbers with a single distribution. Any value with the same share of probability can get into the lower boundary of the requested range and in the upper one. It turns out a huge scatter from the target value.
The normal distribution implies the close position of most generated numbers to the target. Correct the formula to the rational and create an array of data with a normal distribution.
The cost of goods X is 100 rubles. The entire batch produced is subordinate to the normal distribution. Random variable also obeys normal probability distribution.
Under such conditions, the average value of the range is 100 rubles. Let us generate an array and construct a graph with a normal distribution with a standard deviation of 1.5 rubles.
Use the function: \u003d Normo (adhesive (); 100; 1.5).
The Excel program considered what values \u200b\u200bare in the probability range. Since the probability of producing goods with the cost of 100 rubles is maximum, the formula shows the values \u200b\u200bclose to 100 more often than the rest.
Let us turn to the construction of the schedule. First you need to make a table with categories. To do this, share an array for periods:
Based on the data obtained, you can form a diagram with a normal distribution. The values \u200b\u200baxis are the number of variables in the interval, the category axis - periods.
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