[whispering]

I am not able to motivate further, it's just that usually when we talk about random numbers we mean uniformly distributed random numbers. It is not a requirement in a strict sense. It's just the easier way to tell about randomness. We all have an intuitive understanding of rolling a dice or flipping a coin.

[rbanffy]

As a fun example, I used to run load tests for several systems using random numbers distributed under a power law.