Let X 1 ,...,X n be i.i.d. random variables having a stable law distribution with index α, 1 Show that   has the same stable law and   does not exist. Hence, or otherwise, compare with the bootstrap...

Let X₁,...,X_n
be i.i.d. random variables having a stable law distribution with index α,

1 <>

Show that
  has the same stable law and
  does not exist. Hence, or otherwise, compare with the bootstrap distribution of
  which is contended to be normal for large n.