If something is said to be 'random" and yet alwaysfits within a gaussian distribution, can it truly be called

Question

random?

Answer 1

Yes. The randomness is for individual outcomes, not for the shape of the distribution.

Indeed, you can easily convert an event with a Gaussian distribution - or any other continuous distribution - into one with N discrete, equally probable outcomes.

To do this, simply divide the probability space up into N parts each with probability 1/N, and define a new variable whose values are 1, ..., N according to the corresponding intervals of the original random variable. This new variable will take on values 1, ..., N each with probability 1/N, but is exactly as random as the original - it's really just a transformed version of the original.

Randomness means that you can't correlate outcomes, not that you can't specify the distribution.

Answer 2

It all depends what you mean by "fits within a Gaussian distribution". If you always hit Gaussian distribution with the least possible variation, something is fishy. You can test the variation with a Χ-square or similar test. For any given probability that the variation is solely due to chance, you should exceed the critical value for that probability, that portion of the time. If p<0.05, you should fail the Χ-square test 5% of the time. There is no actual test for randomness in a single set.

Answer 3

If i hit keys "randomly" i would still be more likely to hit keys in the center and unlikey to use random sybols that only macs have and i'm likey to stick to english. as for that, i guess statisticly, i'm most likley to hit keys in the home row as thats where my fingers are. so i guess nothing is truly random and the sky is dark. that last part was kinda random...

Answer 4

yes.