math question

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  • hhsilver
    SBR Hall of Famer
    • 06-07-07
    • 7375

    #1
    math question
    More than a month ago someone posed this challenge in players talk :

    (see this thread)>>http://forum.sbrforum.com/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://forum.sbrforum.com/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
    SBR MVP
    • 03-20-10
    • 1351

    #2
    he s stiff
    Comment
    • mathdotcom
      SBR Posting Legend
      • 03-24-08
      • 11689

      #3
      Originally posted by hhsilver
      More than a month ago someone posed this challenge in players talk :

      (see this thread)>>http://forum.sbrforum.com/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://forum.sbrforum.com/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.
      Comment
      • Kemalettin
        SBR MVP
        • 03-20-10
        • 1351

        #4
        hey freak post the answer then
        Comment
        • sharpcat
          Restricted User
          • 12-19-09
          • 4516

          #5
          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.
          Comment
          • hhsilver
            SBR Hall of Famer
            • 06-07-07
            • 7375

            #6
            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.
            Comment
            • hhsilver
              SBR Hall of Famer
              • 06-07-07
              • 7375

              #7
              Originally posted by 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.
              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
              Comment
              • Ganchrow
                SBR Hall of Famer
                • 08-28-05
                • 5011

                #8
                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*pn-1

                = n n+1 * pn+1 | p=0 → 1
                = n n+1

                QED

                Nicely done, hh. YOu get full credit in my book.
                Comment
                • aca
                  SBR MVP
                  • 03-20-06
                  • 2111

                  #9
                  Thanks!
                  Comment
                  • Peeig
                    SBR Wise Guy
                    • 02-06-08
                    • 567

                    #10
                    Ganchrow is back???
                    Comment
                    • Patrick McIrish
                      SBR MVP
                      • 09-15-05
                      • 2864

                      #11
                      Let's all hope so. John, apologize and tender an offer immediately! Thanks.



                      Well done Silver, you get all the credit.
                      Comment
                      • mathdotcom
                        SBR Posting Legend
                        • 03-24-08
                        • 11689

                        #12
                        Ganch I said in a previous thread the answer should have integrals in it.

                        Others made intuitive guesses too, like 1 - (1/2)^n.
                        Comment
                        • hhsilver
                          SBR Hall of Famer
                          • 06-07-07
                          • 7375

                          #13
                          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.

                          Originally posted by 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.
                          )

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

                          http://forum.sbrforum.com/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:

                          Sports betting and handicapping forum: discuss picks, odds, and predictions for upcoming games and results on latest bets.


                          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 .

                          ------
                          Comment
                          • Ganchrow
                            SBR Hall of Famer
                            • 08-28-05
                            • 5011

                            #14
                            Originally posted by 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)
                            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 3rd and 4th definitions of the root noun.
                            Comment
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