Post making contest 6.0

A random variable is said to have a zeta (sometimes called the Zipf) distribution if its probability mass function is given by

P(X=k)=C/k^α+1 k=1,2,...

for some value of α>0. Since the sum of the foregoing probabilities must equal 1, it follows that

C=[∑(1/k)^α+1]^-1

The zeta distribution owes its name to the fact that the function

ζ(s)=1+(1/2)^s+(1/3)^s+...+(1/k)^s+...

is known in mathematical disciplines as the Riemann zeta function (after the German mathematician G.F.B. Riemann).
The zeta distribution was used by the Italian economist V. Pareto to describe the distribution of the family incomes in a given country. However, it was G.K. Zipf who applied zeta distribution to a wide variety of problems in different areas and, in doing so, popularised its use.[/quote]Good math! I'm so impressed that this passes all the rules, at least if you give me more math.[quote="Kíeros"]A very important property of expectations is that the expected value of a sum of random variables is equal to the sum of their expectations. In this section, we will prove this result under the assumption that the set of possible values of the probability experiment--that is, the sample space S--is either finite or countably infinite. Although the result is true without this assumption (and a proof is outlined in the theoretical exercises), not only will the assumption simplify the argument, but it will also result in an enlightening proof that will add to our intuition about expectations. So, for the remainder of this section, suppose that the sample space S is either a finite or a countably infinite set.
For a random variable X, let X(s) denote the value of X when s∈S is the outcome of the experiment. Now, if X and Y are both random variables, then so is their sum. That is, Z=X+Y is also a random variable. Moreover, Z(s)=X(s)+Y(s).