Use the counter example to show that convergence in distribution does not imply convergence in probability.
Let Ω={1, 2}, Ϝ=ρ(Ω), and let P be defined by P({1})=P({2})=1/2.
Let X_n(1)=1, X_n(2)=0 (for all n) and X(1)=0, X(2)=1.
Then show that X_n converges to X in distribution but not in probability.
----------
If anyone helps me, I will be thankful.
Selin