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Random Numbers

Tools to select numbers randomly, make random draws of numbers according to several criteria and let randomness/chance decide.

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Random Numbers -

Tag(s) : Fun/Miscellaneous, Algorithm, Combinatorics

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Random Numbers

Random Numbers Selection

What is a random number? (Definition)

A random number is a number selected at random from an interval. The randomly selected number is usually either an integer or a decimal number.

Most often the number is calculated by computer using pseudo-randomness functions like rand() or random().

How to make a random number selection?

Indicate the type of numbers to draw:

— choice according to an interval: select numbers between $a$ and $b$

Example: Draw $N$ digits between $1$ and $100$

— choice according to a size: select numbers with a certain number of digits

— choice according to a list: select numbers from a given list

Example: A phone number corresponds to N digits from 0 to 9

What is a random number sample without replacement?

A draw without replacement specifies that a picked number can not be picked a second time.

Example: Draws of $3$ numbers between $1$ and $5$ could be $4,2,3$ or $1,5,2$ but never $1,2,2$ (the $2$ having been picked a first time, it is not put back into play)

During a draw without replacement, it is not possible to pick more than $N$ numbers in a range of size $N$

Example: A selection of $100$ numbers between $1$ and $20$ is impossible without replacement

What is a random number sample with replacement?

A draw with replacement specifies that a picked number may be picked one or more times.

Example: Draws of $3$ numbers between $1$ and $5$ could be $4,2,3$ or $1,5,2$ but also $1,2,2$ (the $2$ having been picked a first time, it is put back into play and can stand out)

During a draw with replacement, it is possible to pick more than $N$ numbers in a range of size $N$

Example: A selection of $100$ numbers between $1$ and $20$ is possible with replacement

How to pick only even numbers?

Option 1: list the even numbers (if there are not too many) and draw from this list.

Option 2: Multiply the numbers obtained by 2, they will all be even.

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