Understanding “randomness”

Question

I can\'t get my head around this, which is more random?

rand()

OR:

rand() * rand()

I´m f

Answer 1

It's easy to show that the sum of the two random numbers is not necessarily random. Imagine you have a 6 sided die and roll. Each number has a 1/6 chance of appearing. Now say you had 2 dice and summed the result. The distribution of those sums is not 1/12. Why? Because certain numbers appear more than others. There are multiple partitions of them. For example the number 2 is the sum of 1+1 only but 7 can be formed by 3+4 or 4+3 or 5+2 etc... so it has a larger chance of coming up.

Therefore, applying a transform, in this case addition on a random function does not make it more random, or necessarily preserve randomness. In the case of the dice above, the distribution is skewed to 7 and therefore less random.