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About LinkBacksLet berandom 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
Prove that:
a)
b) If
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 numberthen at least one of the two terms on the right-hand side of the inequality is greater than
Thank you for your help!Originally Posted by Alibiki
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
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