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Expectation homework help

  1. Apr 12, 2010 #1
    Hi I'm going through some presentation material and i cant understand how the following has been derived

    [tex]\sum^{n}_{j=1} \mathbb{E}[ ln(1 +K_{j})] = n \mathbb{E}[ln(1+K_{1})] [/tex]

    Could someone point me in the right direction on why this makes sense ?

    Thanks
     
  2. jcsd
  3. Apr 13, 2010 #2

    mathman

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    Science Advisor

    Re: expectation

    It only makes sense if all Kj have the same distribution, although it could hold (by accident) in more general situations.
     
  4. Apr 14, 2010 #3
    Re: expectation

    ok suppose all [tex]K_{j}[/tex] have exactly the same distribution, I still can see why it makes sense. why does the following hold [tex]\sum^{n}_{j=1} \mathbb{E}[ ln(1 +K_{j})] = n \mathbb{E}[ln(1+K_{1})] [/tex]

    maybe there is something trivial here that i'm missing but i still cant see it
     
  5. Apr 14, 2010 #4

    statdad

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    Homework Helper

    Re: expectation

    If all the [itex] K_j [/itex] have the same distribution, so do all of the [itex] \ln (1+K_j)[/tex], and this common distribution is the same as that of [itex] \ln(1+K_1)[/itex].

    If they have the same distribution, and if the expectations exist, then every term in the first sum is the same.
     
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