[Ezra Halleck]

10. a) Explain law of large numbers and explain how you would used it to find the chance of a head for a bent coin.

As the number of trials is increased, the spread around the mean is narrowed. Hence by flipping the coin dozens or better yet, hundreds of times, you would, with a high probability, get a good idea of its bias, i.e., how much it differs from a fair coin.

[samantharauch]

Professor Halleck,

So, the reason you are able to distinguish if it is a bent coin is because the spread around the mean is narrowed? I understand what you mean, but feel like I would have trouble phrasing it myself. Could you explain a bit more?

Thanks,

Samantha

[Ezra Halleck]

Just so that you can sleep soundly tonight, this question is not on the exam. However, this important issue is at the heart of sampling and I hope to have an opportunity to discuss it more. The idea is basically, the more trials you perform the more likely you are to have got something close to the true value. Let’s suppose for instance that you flip a coin 10 times and get p=.55 and you flip the coin 100 times, and you get p=.45. The real value of p is likely to be much closer to .45 than it is to .55.