This law is confusing me so I'm having some trouble with the problems...
We have two coins: one is a fair coin and the other is a coin that produces heads with probability 3/4. One of the two coins is picked at random, and this coin is tossed n times. Using the Law of Large Numbers, how many tosses suffice to make us 95 percent sure of which coin we have chosen?
Aug 2nd 2009, 11:53 PM
The Law of Large Numbers (Weak, Strong...) tells you that the sample mean converges (in some sense) to the pop mean.
In this case the sample mean is the sample proportion and the population mean is the probability of a head.
I would use the CLT to see if the sample proportion was within 2 st deviations of either .5 or .75.