Suppose that X1, X2, . . . are independent, identically Linnik(α)-distributed random variables, that N ∈ Fs(p), and that N and X1, X2, . . . are independent. Show that p1/α(X1 + X2 + · · · + XN ) is, again, Linnik(α)- distributed.
Remark. The characteristic function of the Linnik(α)-distribution (α > 0) is ?(t) = (1 + |t|α)-1.