Re: sums of discrete uniform random variables

On Sun, 23 Dec 2007 23:35:04 -0800 (PST), Butch Malahide
<fred.galvin@xxxxxxxxx> wrote:

On Dec 24, 1:08 am, quasi <qu...@xxxxxxxx> wrote:
Let X_1, X_2, X_3, ... be independent, identically distributed random
variables, each uniformly distributed on the set {0,..., n-1}. In
other words, each X_i is uniformly distributed mod n.

Prove or disprove:

(X_1 + ... + X_k) mod m is uniformly distributed mod m iff m|n.

Do you really need all those assumptions? Wouldn't it be enough to
assume that one of the variables, say X_1, is uniformly distributed
mod m, and the rest are integer-valued variables with arbitrary
distributions?

Sure -- that's better, provided it's true, and it does seem like it
should be true.

quasi
.

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