What does it mean to draw a number at random from a normal distribution? Why can't you just "draw" numbers at random? Why do you have to draw random numbers from a distribution?

  • $\begingroup$ I think you should thin about this question in reverse. If you draw random numbers (say for example pulling numbers out of a hat) will it follow a distribution? The answer is yes, although you may not know what the distribution is. So to answer your second questions yes you can just "draw" numbers at random. $\endgroup$
    – user25658
    Commented Sep 23, 2013 at 14:54
  • 5
    $\begingroup$ @BabakP Your advice is good, but beware! Not all procedures for creating numbers arbitrarily will have probability distributions. Because this is a subtle concept, here's an explicit example couched in the language of discrete stochastic processes: draw values independently from a Bernoulli$(3/4)$ distribution at times $t\ge 1$ when the integer part of $\log_2(t)$ is even and otherwise draw the values from a Bernoulli$(1/4)$ distribution. What could "the" distribution of this process possibly be? In light of this, one has to question whether your answer to Q2 even makes sense. $\endgroup$
    – whuber
    Commented Sep 23, 2013 at 15:14
  • 6
    $\begingroup$ @Peter Interesting thought; but no: make a plot of the expected mean as a function of $t$ to see what's going on. (Use a logarithmic scale for $t$.) There are deep conceptual issues involved here: randomness is not arbitrariness, nor is all randomness describable with a (fixed) probability distribution. $\endgroup$
    – whuber
    Commented Sep 23, 2013 at 16:14
  • 3
    $\begingroup$ Can you explain what you mean by "draw numbers at random?", without implying an underlying distribution? I must admit to being skeptical that this could even be a coherent notion. $\endgroup$
    – Glen_b
    Commented Sep 24, 2013 at 8:02
  • 1
    $\begingroup$ Phil, finding numbers in your head is demonstrably not random. Randomness implies certain properties that subjective generation of numbers does not have. $\endgroup$
    – whuber
    Commented Sep 24, 2013 at 14:43

1 Answer 1


Because you want to produce a "sample" that is representative of the type of distribution that you wish to compare with your real data and its expected distribution as well, for example, uniform, normal, exponential, and a whole host of others.

  • $\begingroup$ And there isn't an alternative. You cannot sample without some distribution by default. Most imperative computer languages have a standard library function that produces random numbers in a uniform distribution between 0 and 1. $\endgroup$
    – JRideout
    Commented Sep 24, 2013 at 15:36

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.