Do Infinity and Statistics Always Go Hand in Hand?

In summary, the conversation discusses the concept of infinity and probability, specifically in relation to rolling a die an infinite number of times and the likelihood of rolling a 6. The conclusion is that while it is possible to roll a 6 with certainty, it is not guaranteed, as probability does not always translate to real-life outcomes. The concept of "almost surely" is also mentioned as a way to express the high likelihood of a certain outcome.
  • #1
red apple
2
0
Hi there, I have a question regarding infinity and statistics. (I hope there aren't too many questions with infinity on these forums)

I was wondering if you had some simple procedure, like say rolling a six sided die, and said you did this an infinite amount of times, would it be valid to say eventually you will roll a 6? Of course this is an ideal situation where each side has an equal chance of being rolled.

I'm wondering if it is accurate to say you will eventually have any outcome occur (assuming it is possible on any individual trial, no matter how unlikely)

Is this even valid considering its not really possible to actually have this happen in real life?

Also just for fun, what about an example taken to the extreme like an infinite amount of monkies all writing on typewriters, assuming they at least type something will at least one type a Shakespeare play exactly? Will an infinite amount type a Shakespeare play?

Thank you.
 
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  • #2
red apple said:
I was wondering if you had some simple procedure, like say rolling a six sided die, and said you did this an infinite amount of times, would it be valid to say eventually you will roll a 6? Of course this is an ideal situation where each side has an equal chance of being rolled.

Not really, but you can say that the chance of rolling a 6 is 100% (exactly).

red apple said:
Is this even valid considering its not really possible to actually have this happen in real life?

Sure. We don't have perfectly fair dice in real life, either.

red apple said:
Also just for fun, what about an example taken to the extreme like an infinite amount of monkies all writing on typewriters, assuming they at least type something will at least one type a Shakespeare play exactly? Will an infinite amount type a Shakespeare play?

With probability 1, yes.
 
  • #3
Note, however, that when you are dealing with something happening an infinite number of times (or working with continuous probability distributions), a probability of 1 does NOT mean it must happen nor does a probability of 0 mean it won't happen. It is possible to roll a die an infinite number of times and NOT get a "6". It is even possible to roll a die an infinite number of times and always get a "2" (Assuming that it is possible to roll a die and infinite number of times!) even though the probability of rolling a "6" is 1 and the probability of rolling all "2"s is 0.
 
  • #4
Quite correct, Halls. I should have pointed that out.
 
  • #5
CRGreathouse said:
Not really, but you can say that the chance of rolling a 6 is 100% (exactly).

I believe in mathematics we say that you will almost surely roll a 6.

http://en.wikipedia.org/wiki/Almost_surely
 
  • #6
Diffy said:
I believe in mathematics we say that you will almost surely roll a 6.

http://en.wikipedia.org/wiki/Almost_surely

I say both "...with probability 1." and "...almost surely.", though I prefer the former. Only pedagogically do I say "The chance of ... is 100%."
 

FAQ: Do Infinity and Statistics Always Go Hand in Hand?

What is infinity in statistics?

Infinity in statistics refers to the concept of having an infinitely large sample size or population. This means that the data being analyzed is representative of an entire population and can provide more accurate and reliable results.

How is infinity used in hypothesis testing?

Infinity is used in hypothesis testing to determine the probability of obtaining a certain result by chance. By assuming an infinitely large sample size, the null and alternative hypotheses can be compared to determine the likelihood of obtaining the observed data.

What are the limitations of using infinity in statistics?

The concept of infinity in statistics is mostly theoretical and not practical. In real-world scenarios, it is impossible to have an infinitely large sample size or population. Additionally, using infinity in calculations can lead to complex and unreliable results.

What is the difference between infinity and undefined in statistics?

Infinity refers to a value that is larger than any number that can be expressed, while undefined refers to a value that has no defined meaning or cannot be determined. In statistics, infinity is often used to represent a very large value, while undefined may refer to missing or incomplete data.

How does infinity impact the interpretation of statistical results?

The use of infinity in statistics can impact the interpretation of results by providing a more accurate representation of a population. It can also help identify statistical significance and the probability of obtaining certain results. However, it is important to keep in mind the limitations and potential inaccuracies associated with using infinity in statistics.

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