9.3.1  Producing uniformly distributed random numbers: rand random alea hasard sample

The rand command produces random numbers, chooses random elements from a list, or creates functions that produce random numbers.
random and hasard are synonyms for rand.

To produce random real numbers:

• rand takes two optional arguments.
  • Optionally, a and b, two real numbers. By default, a=0 and b=1.
• rand([a,b]) returns a number in [a,b) randomly and with equal probability.

Examples.

• Input:
  rand()
  (to produce a random number in [0,1)). Output (for example):

  0.528489416465

• Input:
  rand(1,1.5)
  (to produce a random number in [1,1.5)). Output (for example):

  1.0012010464

To produce random integers:

• rand takes one argument:
  n, an integer.
• rand(n) returns a random integer in [0,n) (or (n,0] if n is negative).

Example.
Input:

Output (for example):

You can then use rand to find a random integer in a specified interval; if you want an random integer between 6 and 10, inclusive, for example, you can enter:
Input:

Output (for example):

Another way to get a random integer in a specified interval is with the randint command.

• randint takes two arguments:
  n₁ and n₂, two integers.
• randint(n₁,n₂) returns a random integer between n₁ and n₂, inclusive.

Example.
Input:

Output (for example):

To make a function which produces random numbers:

• rand takes one argument:
  a..b, a range with real numbers a and b.
• rand(a..b) returns a function which will generate a random number in the interval from a to b.

Example.
Input:

Output (for example):

To choose elements without replacement:

• rand takes two or three arguments:
  • p, a positive integer.
  • Either: n₁ and n₂, two integers.
  • or: L, a list.
• rand(p,n₁,n₂) returns a list of p distinct random integers from n₁ to n₂.
• rand(L) returns p elements without replacement from the list L.

Examples.

• Input:
  rand(2,1,10)
  Output (for example):

  ⎡ ⎣

  2,9

  ⎤ ⎦

• Input:
  rand(3,["a","b","c","d","e","f","g","h"])
  Output (for example):

  ⎡ ⎣

  "e","g","a"

  ⎤ ⎦

• The list can have repeated elements.
  Input:
  rand(4,["r","r","r","r","v","v","v"])
  Output (for example):

  ⎡ ⎣

  "r","v","v","r"

  ⎤ ⎦

The sample command will also randomly select items from a list without replacement.

• sample takes two arguments:
  • L, a list.
  • p, an integer.
• sample(L,p) returns a list of p items chosen randomly from L, without replacement.

Note that with the sample command, the list comes first and then the integer.

Example.
Input:

Output (for example):