|Jan16-12, 11:54 PM||#69|
Coin flip probabilities and relevance
"The problem with probability is that there are some certainties about it ... The fallacy is the whole concept of infinity."
If you need to have certainties, and you outright reject the concept of infinity, then the study of probabilities is going to lead you to a stone wall.
|Jan17-12, 12:10 AM||#70|
For many practical purposes the strong law tells us a lot about the kind of limiting probabilities for large enough sample sizes as it would for an infinitely large number of them.
To understand this its best to think of the derivative of 1/x. If x is big enough then any change thereafter is not going to have much of an effect if the observations up to that point reflect a mostly unbiased sample. If the sample is highly biased then we can't necessarily do this, but for most purposes "large enough" samples will provide a distribution that is good enough to represent the true distribution for "infinite" sample sizes.
|Mar2-12, 04:01 AM||#71|
I know this thread is over 8 years old, but this reply is for the benefit of someone like me who stumbles across it. Plus I think I can explain it in a more simpler manner, especially for those with basic stats knowledge.
Then you carry on and do another 1,000,000 coin flips, but this time you get exactly 500,000 heads and 500,000 tails. So no increase in tails from a pressure wave. But, even without the tail pressure wave your graph has now moved to a 50.4/49.6 distribution.
What's happened is that you've simply increased the sample size and that has reduced the effect of the 9000 heads. Hopefully you can now see that the wave patterns tending towards the 50/50 distribution, are caused by the increase in samples and not an increase in heads or tails through a pressure wave.
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