Let be random variables on the same probabilty field. Assume that and (denotes convergence in probabilty).
Prove that:
a) .
b) If (with probabilty 1), then .
I would really appreciate if you could help me.
Thank you in advance!
Let be random variables on the same probabilty field. Assume that and (denotes convergence in probabilty).
Prove that:
a) .
b) If (with probabilty 1), then .
I would really appreciate if you could help me.
Thank you in advance!
You might try one of the standard mathematical tricks: Do nothing, but do it in a smart way!
In this case one such trick is to write
and insert this in the salient difference
Invoking the Triangle inequality you can write
If the left-hand side of this inequality is larger than some small positive number then at least one of the two terms on the right-hand side of the inequality is greater than