Question

Which is more random?

rand()

OR

rand() + rand()

OR

rand() * rand()

Just how can one determine this? I mean. This is really puzzling me! One feels that they may all be equally random, but how can one be absolutely sure?!

Anyone?

Answer 1

The concept of being “more random” doesn’t really make sense. Your three methods give different distributions of random numbers. I can illustrate this in Matlab. First define a function f that, when called, gives you an array of 10,000 random numbers:

f = @() rand(10000,1);

Now look at the distribution of your three methods.

Your first method, hist(f()) gives a uniform distribution:

Your second method hist(f() + f()) gives a distribution which is peaked in the centre:

Your third method hist(f() .* f()) gives a distribution where numbers close to zero are more likely: