Consider the t-distribution with m degrees of freedom. Show that for this distribution, the moment generating function M(t) is not finit for any real t, and, hence, comment on the rate of convergence...

Consider the t-distribution with m degrees of freedom. Show that for this distribution, the moment generating function M(t) is not finit for any real t, and, hence, comment on the rate of convergence for the t-statistic. Another counterexample is the classical Cauchy distribution for which the density function is given by
  Show that for this distribution, no positive moment of order 1 or more is finite and, hence, none of the probability inequalities discussed so far apply.