# Probabilistic(random) within a bound deterministic region?

I had a discussion with a professor, who came with this thought: When you randomly sample from a Normal distribution of fixed mean and variance, how can you claim that the sample is random when actually the samples are from a fixed distribution? Are those samples really random? or "random"? I will appreciate if this line of thought can be discussed further. I happen to somewhat agree with his thoughts, am I or he missing some fundamental things here?

PS: When you do this operation on a computer you call it pseudo-random. Assume that a person sampled the samples instead of a computer.

• They're random but not all numbers have an equal probability of coming up. Numbers closer to the mean are more likely to come up. It's not a "uniform" distribution.
– user935
Dec 9, 2017 at 0:07
• "When you randomly sample from a Normal distribution of fixed mean and variance, how can you claim that the sample is random" <- this is too easy to answer; I don't get it. Given you randomly sample, your sample is obviously random (if it weren't, how is it you can say you randomly sampled?). It's just tautological. What is your question? Dec 9, 2017 at 11:25
• Also: "When you do this operation on a computer you call it pseudo-random." ...this only follows if your computer uses a pseudo-random number generator. Computers have RNG's that aren't PRNG's (which works by collecting "entropy" from the environment using inputs). But ignoring that, sure, computers are PRNG's... are you analogously asking then if people are good sources of randomness maybe? Dec 9, 2017 at 11:30
• I've read that people are bad sources for generating random results when they're told to do something randomly. Dec 9, 2017 at 13:37
• @barrycarter a normal random variable can be constructed using uniform random variable. Dec 11, 2017 at 19:08