Re: sums of discrete uniform random variables

On 2007-12-24 02:08:38 -0500, quasi <quasi@xxxxxxxx> said:

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.

Seems true by argument of symmetry. How can probability distinguish between any two distinct values in {0, ..., m-1}?

--

-kira

.

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