Let X have density function given by fX (x) = {

Show that the mean of X is finite but that all higher-order moments are infinite. Find an expression for the density of Y = 1/X and show that all moments and cumulants are finite.

Let μ′rs = E(X rY s

) be the joint moment of order r+s (using the power notation of Section 2.5). Show that μ′rs

= 2 but that the corresponding cumulant, κ21, is infinite.