distributed) with 'cauchy' distribution. If X is a random variable

with cauchy distribution, then for all u in R:

E[exp(iuX)]=exp(-|u|).

So E[exp(iu(Sn/n))]=E[prod(exp(i(u/n)Xj))]=prod(E[i(u/n)Xj])

=prod(exp(-|u|/n))=(exp(-|u|/n))^n=exp(-|u|)

(where we have used the independence for E[prod.. = prod E[.. )

so the characteristic function of Sn/n is also that of a cauchy

distributed variable for all n.

Regards. Noel