Approaching 1/2 Probability

[uncool]

6 minutes ago, Conjurer said:

If you gave me an equation, I could plug probabilities or fractions into, that made the final result approach the same probability by summing up more possible outcomes in a row, I would recommend you for the Nobel Prize in mathematics.

It would be like what calculus did to gravity, and you would be the next Isaac Newton of probabilities.   

1) Mathematics has no Nobel Prize.

2) The proof has existed for centuries. As I have told you repeatedly. And as Ghideon has been more than willing to provide data for, and as I have been more than willing to provide data for.

For any epsilon and delta, there exists an N such that for n > N, Pr(|Y_n - p| > epsilon) < delta

Equivalently, sum_{n*(p - epsilon) < i < n*(p + epsilon)} Pr((sum X_j) = i) > 1 - delta

Edited September 18, 2019 by uncool

[Conjurer]

8 minutes ago, uncool said:

1) Mathematics has no Nobel Prize.

I am sure they would make an exception. 

Well, I still don't know how I could plug probabilities into an equation to sum an increasing number of outcomes to obtain a result, where the average outcome is the same as the probability of that single event occurring.

I see no way the equations you provided could accomplish that.  Everytime I find the probability of any event occurring in succession, I only get a lower probability of that event occurring.  That is still all I know from the information you have provided.  

[uncool]

1 minute ago, Conjurer said:

I am sure they would make an exception. 

"They" would not, as "they" have not in the past 118 years. 

2 minutes ago, Conjurer said:

Well, I still don't know how I could plug probabilities into an equation to sum an increasing number of outcomes to obtain a result, where the average outcome is the same as the probability of that single event occurring.

You could try reading my post to find out. Or actually learning probability theory rather than making pronouncements about it.

Choose any N, and some small epsilon. Then:

For any epsilon and delta, there exists an N such that for n > N, Pr(|Y_n - p| > epsilon) < delta

Equivalently, sum_{n*(p - epsilon) < i < n*(p + epsilon)} Pr((sum X_j) = i) > 1 - delta

Equivalently, sum_{n*(p - epsilon) < i < n*(p + epsilon)} nCi * p^i * (1 - p)^j > 1 - delta.

So take n large (say, larger than 100*(p - p^2)/epsilon^2), and find sum_{n*(p - epsilon) < i < n*(p + epsilon)} nCi * p^i * (1 - p)^j. I claim it will always be larger than 99%. 

7 minutes ago, Conjurer said:

I see no way the equations you provided could accomplish that.

Then explain what in them you disagree with, or think doesn't apply. What you've written shows no indication you even read what I wrote (especially since most of what I wrote are inequalities, not equations). 

8 minutes ago, Conjurer said:

Everytime I find the probability of any event occurring in succession, I only get a lower probability of that event occurring. 

Because, once again, it's about looking in a range.

8 minutes ago, Conjurer said:

That is still all I know from the information you have provided.  

Every indication shows the problem is on the receiving end here, since you have failed to show that you even read what I wrote.

[Conjurer]

10 minutes ago, uncool said:

Because, once again, it's about looking in a range.

Every indication shows the problem is on the receiving end here, since you have failed to show that you even read what I wrote.

Who is to say what range we should be looking in?

It was incredibly hard to read, because you didn't use latex format.  Then you didn't define the variables you used in a way I could understand.  

I said at the start of the thread, I just started teaching 7th grade probabilities.  I never had to take probabilities in my past, because I was told that this proof never existed.  Then apparently the Common Core Standards have introduced it into the curriculum, despite that from my knowledge.  

[uncool]

1 minute ago, Conjurer said:

Who is to say what range we should be looking in?

The statement of the theorem itself, as I have repeatedly shown.

5 minutes ago, Conjurer said:

It was incredibly hard to read, because you didn't use latex format. 

For that I apologize; the forum changed software a couple years ago in a really frustrating way, and I still haven't really tried to learn how the new LaTeX embedding works. 

9 minutes ago, Conjurer said:

Then you didn't define the variables you used in a way I could understand.  

Then ask about them.

9 minutes ago, Conjurer said:

I said at the start of the thread, I just started teaching 7th grade probabilities.  I never had to take probabilities in my past, because I was told that this proof never existed. 

1) That really is a bad reason for never having had to take it.

2) Either you misunderstood, or you were misinformed. 

3) If you've never taken probability before, you should not be making pronouncements on it. 

4) To be honest, you should learn the basics of probability theory before teaching it. 

Probability theory is a very well-developed field of math. The theorem you are trying to talk about is one of the most basic theorems in statistics - one of the subfields of probability - and one of the most necessary. 

[hypervalent_iodine]

!

Moderator Note

This is not an appropriate outlet for this topic, this being a section dedicated to mainstream and accepted science / math. Conjurer, since you insist on arguing alternatives, this thread is closed. I would recommend you take the time to review the posts here and go away and review some basics.