[hhsilver]

More than a month ago someone posed this challenge in players talk :

(see this thread)>>http://www.sportsbookreview.com/forum/players-ta...-question.html

Question in post 1. my answer on post 3.

The "math guy" who started the thread never came back to it even though I bumped it a couple times.

I really want to know if I'm correct. If not, I would like to know the answer and have it explained.

I started another thread , http://www.sportsbookreview.com/forum/players-ta...athdotcom.html ,
to try to get him to respond. He did with simply a "wrong" --- no correct answer, no explanation.

I believe my answer may be correct and would like to show how I got it. If it's not correct , maybe someone here could show
me why and give the solution.
Thanks to any real math guys here who may care to respond.

[Kemalettin]

he s stiff

[mathdotcom]

More than a month ago someone posed this challenge in players talk :

(see this thread)>>http://www.sportsbookreview.com/forum/players-ta...-question.html

Question in post 1. my answer on post 3.

The "math guy" who started the thread never came back to it even though I bumped it a couple times.

I really want to know if I'm correct. If not, I would like to know the answer and have it explained.

I started another thread , http://www.sportsbookreview.com/forum/players-ta...athdotcom.html ,
to try to get him to respond. He did with simply a "wrong" --- no correct answer, no explanation.

I believe my answer may be correct and would like to show how I got it. If it's not correct , maybe someone here could show
me why and give the solution.
Thanks to any real math guys here who may care to respond.

Then show it. No points for throwing a guess out there. Unreal you do not give up, you must be really fukkin barreled in.

[Kemalettin]

hey freak post the answer then

[sharpcat]

I am not sure that I understand the problem trying to be solved

But I would conclude that your answer is wrong because he is asking for the highest number and your solution is going to return a percentage.

[hhsilver]

ok - by show it, i guess you mean how i got it. I didn't think you were interested. About the barrelled in, I am not pressing this for the points, but for the answer. I haven't been able to find anything to verify my answer.

here is why my answer is n/(n+1) ........

for the uniform dist you described, I believe the expected result of n picks would have them be evenly spaced in the interval (in this case the interval is [0,1]

1 pick >>>> exp pick is .5 , exp max is 1(1+1) = .5
2 picks >>> exp results are .33333.. , .6666.... , exp max is 2/(2+1) = .66666
..... and so on..
n picks >>> exp results are n evenly spaced points on the interval......, exp max is the largest of these, which is n/(n+1)

I would appreciate your thoughts on this .... if it's wrong, please explain what the answer should be.

[hhsilver]

I am not sure that I understand the problem trying to be solved

But I would conclude that your answer is wrong because he is asking for the highest number and your solution is going to return a percentage.

not true ... my answer is a number, not a pct.

Notice the interval is 0 to 1.

n/(n+1) is a number in that interval

[Ganchrow]

n n+1 is of course correct, just as hhsilver has quite cleverly intuited.

No clue why mathdotcom gave him such a hard time.

But just for shits and giggles, a rather informal late night mathematical proof might read something like this:

We're looking for the E(sup(Xk)) where Xk is a vector of k realizations from the uniform distribution.

For the degenerate case of k=1, the pdf(sup(X1)) = pdf(X1) = 1. Hence:

= 1 2 * p² | p=0 → 1
= 1 2

So E(sup(X1)) = E(X1) = 1 2

For k=2:

Pr(sup(X2) = p ∈ [0,1] )
= Pr( (x(1) ≤ p AND x(2) = p) OR (x(1) = p AND x(2) ≤ p) ) (this is the key step)
≈ 2*p*Δ

Hence:

= 2 3 * p³ | p=0 → 1
= 2 3

Continuing with the same logic, it's clear that for k=n:

Pr(sup(Xn) = p ∈ [0,1] )
≈ n*p^n-1*Δ

= n n+1 * pⁿ⁺¹ | p=0 → 1
= n n+1

QED

Nicely done, hh. YOu get full credit in my book.

[aca]

Thanks!

[Peeig]

Ganchrow is back???

[Patrick McIrish]

Let's all hope so. John, apologize and tender an offer immediately! Thanks.



Well done Silver, you get all the credit.

[mathdotcom]

Ganch I said in a previous thread the answer should have integrals in it.

Others made intuitive guesses too, like 1 - (1/2)^n.

[hhsilver]

Welcome back, Ganch. Thank you for verifying my answer and for providing a proof.
I am not sure "intuitive" is the right word. I guess it depends on the def of intuitive/intuition.
One def is:
intuition:
instinctive knowing (without the use of rational processes)

I don't think that applies in this case because I understand expectation and unform dist. I got my answer using rational processes based on my knowledge of those concepts. But I won't quibble with it being called intuition in the sense that my professors were fond of saying something was "intuitively obvious" when they wanted to skip a tedious proof of the "obvious".
What I didn't like was mathguy equating "intuition" with a "wild guess". I realize I didn't offer a proof , but surely my reasoning indicates it wasn't a wild guess.

Anyway, it's great to have you back. You were missed.

I want to say a little more. I hope other will read this and follow the links to get the full story.

Ganch I said in a previous thread the answer should have integrals in it.

Others made intuitive guesses too, like 1 - (1/2)^n.

)

This is simply not true. See the original question (unedited as of this writing) here:

http://www.sportsbookreview.com/forum/players-ta...-question.html.

No mention was made of using integration. A question was asked , the answer was given and ignored even after bumps and a pm.

I started two other threads to try to get the answer:

this thread and another one:

http://www.sportsbookreview.com/forum/players-ta...athdotcom.html

Notice, at one point, that mathguy said my answer was "wrong" . Then after I explained , at his request, how I got it, he said , still without saying the answer was correct, I had to use an integral. Here is his first mention of integrals - not in the original question as the quote above suggests.

I liken this to the following:

mathguy :: what is the area bounded by the x-axis, y=4, x=6 and x=11?

responder:: (thinking - hey that's a rectangle) area is 4x5 = 20.

mathguy :: wrong!!!! you didn't integrate .

------

[Ganchrow]

Welcome back, Ganch. Thank you for verifying my answer and for providing a proof.
I am not sure "intuitive" is the right word. I guess it depends on the def of intuitive/intuition.
One def is:
intuition:
instinctive knowing (without the use of rational processes)

intuition

1. direct perception of truth, fact, etc., independent of any reasoning process; immediate apprehension.
2. a fact, truth, etc., perceived in this way.
3. a keen and quick insight.
4. the quality or ability of having such direct perception or quick insight.

I was using the verb intuit more in the sense of the 3^rd and 4^th definitions of the root noun.