1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Problem with the mean

  1. Apr 22, 2013 #1
    Hello. I have a problem with one task. The task is:

    Suppose that you playing the game. You have n moves. on each move you win the game with probability p. Your winning amount is equal to move number. For example if you win in first move your winning amount is 1, if you win in n move, your winning amount is equal to n, and if you not win, your winning amount is 0. Need to prove that average winning amount is: (1+n(1-p)^n+1-(n+1)(1-p)^n)/p

    My try:

    1/n [itex]\sum[/itex] k*p(1-p)^k-1, for k=1 to n.
    And tryed to do something but nothing goes on. For example:
    1/n(n*p*(1-p)^n-1+(n-1)*p*(1-p)^n-2+...+(n-n+1)*p*(1-p)n-n
    but cant get the right answer.
    Thanks for helping.
     
  2. jcsd
  3. Apr 22, 2013 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    hello trenekas! :smile:

    (try using the X2 button just above the Reply box :wink:)

    what is ∑ kak-1 ? :smile:

    (and why are you dividing by n ?)
     
  4. Apr 23, 2013 #3
    ok i dont need divide by n :) :D but later ill try to solve that because now i'm in the university lol. when i'll back home :D
     
  5. Apr 23, 2013 #4
    Last edited: Apr 23, 2013
  6. Apr 23, 2013 #5

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    what does kak-1 remind you of? :wink:
     
  7. Apr 23, 2013 #6
    derivative of a^k:D ok thanks. now ill try myself.
     
    Last edited: Apr 23, 2013
  8. Apr 23, 2013 #7
    ok. its time to ask the help :D
    after few rearrangements:
    p * Ʃ k(1-p)k-1
    So k(1-p)k-1=((1-p)k)'
    First of all i calculated the sum of ((1-p)k)
    Ʃ((1-p)k)= (1-(1-p)n+1)/p
    When calculated derivative of that:
    -(n+1)(1-p)n*p-1(1-(1-p)n+1)/p2
    And all this multiply by p.
    And i got:
    -(n+1)(1-p)n*p-1(1-(1-p)n+1)/p=-(n+1)(1-p)n*p-1+(1-p)n+1)/p
    but it is different than i need to get. Where is mistake? Or no mistake? Thanks
     
  9. Apr 23, 2013 #8

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    hi trenekas! :smile:

    it's a bit difficult to tell, because you're using 1-p instead of a,

    but i think if you replace the p in …
    by p-1, and then adjust the rest to make up for it, you'll get the same as wolfram
     
  10. Apr 23, 2013 #9
    but i cant replace because of rules of composition functions. maybe somwhere else is mistake. :confused:
     
  11. Apr 23, 2013 #10

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    yes you can, just subtract (n+1)(1-p)n from the first part, and add it to the second part (total zero)
     
  12. Apr 23, 2013 #11
    oh :D thanks!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Problem with the mean
Loading...