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Stochastic Convergence Watch

1. I realise it's 2:40 am, and I've been working since midday, so a lack of sleep is probably hindering my ability to tackle this question.
But even since this evening, I haven't had a clue.

I have my notes in front of me, I have tried every avenue, from the Law of Large Numbers, to Chebyshev's Inequality, and I just cannot seem to find a starting point.

I would post workings, but I haven't found a way to start this.
I'm not looking for an answer, merely a push in the right direction, so if anyone could help, I would really appreciate it
2. Starting point is to note that the statement is obvious. Let n tend to infinity for each expression you have there, clearly P(8) and P(11) are tending to 0 and P(3) tending to 1 just taking normal limits.

You can now use that information to come up with a more formal epsilon proof.
3. (Original post by Swayum)
Starting point is to note that the statement is obvious. Let n tend to infinity for each expression you have there, clearly P(8) and P(11) are tending to 0 and P(3) tending to 1 just taking normal limits.

You can now use that information to come up with a more formal epsilon proof.

Okay, I have spent this week really trying to do it, but have got nowhere.

There was a part i) to this question:

Now, this is how I answered it:

I emailed my lecturer about part ii), and got this as a response:

I am really sorry for such a long post, but I wanted to show exactly what I've done, and what it is I'm not understanding.
If I calculated then I can get it so that:

However, that is not going the way that is suggested, and even then, I don't know what to do with that

I really am stuck on this

4. Am I even close?

I'm planning on going in to uni tomorrow. I went in today to see him, but he'd gone home, and if he isn't in tomorrow, as it is due in monday, I don't know how I'll do it
5. Sorry, I'm not very good at this stuff, hopefully someone else can help.

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Updated: April 12, 2013
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