mathematics

Random number

Random number is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Random number rather than just read about it. In short: A random number is generated by a random (stochastic) process such as throwing dice. Individual numbers cannot be predicted, but the likely result of generating a large quantity of numbers can be predicted by specific mathematical series and statistics.

Key takeaways

Random number belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Random number to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Random number from memory before moving on to harder problems.

Reference excerpt

A random number is generated by a random (stochastic) process such as throwing dice. Individual numbers cannot be predicted, but the likely result of generating a large quantity of numbers can be predicted by specific mathematical series and statistics.

Algorithms and implementations Random numbers are frequently used in algorithms such as Knuth's 1964-developed algorithm for shuffling lists. (popularly known as the Knuth shuffle or the Fisher–Yates shuffle, based on work they did in 1938). In 1999, a new feature was added to the Pentium III: a hardware-based random number generator. It has been described as "several oscillators combine their outputs and that odd waveform is sampled asynchronously." These numbers, however, were only 32 bit, at a time when export controls were on 56 bits and higher, so they were not state of the art.

Common understanding In common understanding, "1 2 3 4 5" is not as random as "3 5 2 1 4" and certainly not as random as "47 88 1 32 41" but "we can't say authoritavely that the first sequence is not random ... it could have been generated by chance." When a police officer claims to have done a "random .. door-to-door" search, there is a certain expectation that members of a jury will have.

Real world consequences Flaws in randomness have real-world consequences. A 99.8% randomness was shown by researchers to negatively affect an estimated 27,000 customers of a large service and that the problem was not limited to just that situation.

See also Algorithmically random sequence Quasi-random sequence Random number generation Non-uniform random number generation Random real Random sequence Random variable Random variate

References

Illustrations

Worked examples

Example 1 — a first encounter with Random number

Start with the simplest possible case. Write down what Random number claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Random number before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Random number ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Random number

In research: Random number appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Random number in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Random number is common in secondary-school and first-year university syllabi. It links to neighbouring topics Permutations, so understanding it makes those chapters shorter.
In everyday life: Look for Random number outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Random number in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Random number means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Random number out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Random number in simple terms?

Why does Random number matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Random number?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Random number.