Hi there,
I'm currently going through a review worksheet and running into a couple of questions.
For the question:
Let Xn be the sum of n independent fair die rolls:
1) Find the largest constant α such that limn→∞ P(Xn ≥ αn) > 0.
2) For the α above, find the largest constant β such that limn→∞ P(Xn > αn + nβ ) > 0.
My thinking is: given n independent fair die rolls, the highest sum possible is 6n. Therefore, α should be 6, because the probability of hitting P(Xn ≥ 6n) is still > 0.
However, I don't quite understand how to answer the second problem.
Any help would be greatly appreciated!
I'm currently going through a review worksheet and running into a couple of questions.
For the question:
Let Xn be the sum of n independent fair die rolls:
1) Find the largest constant α such that limn→∞ P(Xn ≥ αn) > 0.
2) For the α above, find the largest constant β such that limn→∞ P(Xn > αn + nβ ) > 0.
My thinking is: given n independent fair die rolls, the highest sum possible is 6n. Therefore, α should be 6, because the probability of hitting P(Xn ≥ 6n) is still > 0.
However, I don't quite understand how to answer the second problem.
Any help would be greatly appreciated!