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Statistics expectation of discrete variable.

  1. May 13, 2013 #1
    Hi,

    1. The problem statement, all variables and given/known data

    How may I find to what number Ʃ(m=1 to ∞) m/2m-1 converges?
    Further, suppose I know it converges to 4, why would then E(Y), given that P(Y) = 1/2m-1, be equal to 2 (thus asserted the answer) and not 4?

    2. Relevant equations



    3. The attempt at a solution
    I am really not sure how to analyse that series. I have managed to determine, through the ratio test, that it indeed converges, but I am not sure how to break it down so that it could be easily determined to what number it converges. I'd truly appreciate some assistance.
     
  2. jcsd
  3. May 13, 2013 #2

    tiny-tim

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    hi peripatein! :smile:
    calculus? :wink:
    i don't understand :redface:

    what is Y ? :confused:
     
  4. May 13, 2013 #3
    Y is just a discrete variable for which the probability is P(Y) = 1/2m-1. But how is E(Y) 2 (based on the answers in the book)?! Why is it not 4?
    And I realise calculus would render the evaluation of Ʃ(m=1 to ∞) m/2m-1 possible, yet I am not sure how to break it down. Could you help?
     
  5. May 13, 2013 #4

    tiny-tim

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    hi peripatein! :smile:
    start by writing f(x) = ∑ mx-(m-1) :wink:
    do you mean P(Y=m) ? :confused:
     
  6. May 14, 2013 #5

    haruspex

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    Do those probabilities add up to 1?
     
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