You are dropping a lot of context here. In the first instance, every second we get a 'truly fair' random sample from all the messages in that second. Going fr

You are dropping a lot of context here. In the first instance, every second we get a 'truly fair' random sample from all the messages in that second. Going from there to eg a 'truly fair' random sample from all the messages in a minute is not trivial. And it's not even possible just from the samples, without auxiliary information.