I know this problem is not really a statistical problem but more a math problem, but I am sure you can help me though:
I have a probability function dependend on time $t$:
(the factor a is just a scaling factor)
So if I plot this function, I can see, that for $t$ tending to infinity the probability approx is $0.5$. So now I want to show this in a mathematical way, so I thought the limes would be appropriate for this case? Is this true? So how can I apply lim in this case (I am not good in math I know). Thanks.