Extend the results in the previous exercise to the case where An is a stochastic matrix, by making   Let   be i.i.d. random variables with density   Define the sample median    where   Show that   is...

Extend the results in the previous exercise to the case where An is a stochastic matrix, by making

Let
  be i.i.d. random variables with density

Define the sample median
   where
  Show that
  is a strongly consistent estimator of θ. Also, let
  Show that
  has asymptotically a normal distribution with zero mean and a finit variance.