If X_n tends to 2 almost surely as n tends to infinity.
Which of the follwoing if either are equivalent to this?
P(X_n tends to 2 as n tends to infinity)=1
or
P(X_n tends to 2 )=1 as n tends to infinity
Any help would be greatly appreciated
If X_n tends to 2 almost surely as n tends to infinity.
Which of the follwoing if either are equivalent to this?
P(X_n tends to 2 as n tends to infinity)=1
or
P(X_n tends to 2 )=1 as n tends to infinity
Any help would be greatly appreciated
The first one. Almost sure means that the probability will be eventually one (denoted by the equality sign, while the limit is WITHIN the brackets). The second expression is convergence in probability, so the expression approaches one when n goes to infinity but never actually gets there.