I'm trying to prove the following :
I've been trying various methods, but I cannot find a general way to prove this. I guess it requires playing with inequalities and common sense, but I already am having difficulties proving it when (I've been separating it in two cases, the first one being , then I add both to find the desired probability). Does anyone have a general proof for this ?Say you are given a set of random numbers with . Prove that . That is, prove that the sum of all the random numbers modulo has an equal chance of being any number between and .