[awegio]

In more formal terms, since it is a uniform distribution you can write

  random(x) = random()*x

then you can easily see that

  random(random(random())) = random()*random()*random()

The resulting distribution is not equal to random()^3, because e.g. the probability that all 3 random calls give you a number <0.5 is only 0.125.

[hedora]

Oh. Thanks for the explanation, but I thought random was taking a seed, which would have made this much cooler, like this:

https://www.jstatsoft.org/article/download/v007i03/892

[ibrahimbeladi]

It depends on the language, some languages like JS does not take an argument. So, it is language-specific.

[jwsteigerwalt]

Clear and simple explanation

[IIAOPSW]

Took me a moment to understand that by random()^3 you meant the output of the random function to the power of 3, not some temporary function which we name "random^3" since that's also how we build it.