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Math Help - Expected Value of Sigma of Geometrically distributed parameter y

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    Expected Value of Sigma of Geometrically distributed parameter y

    What will be the expected value of the sum of geometrically distributed parameter y.

    E [Sigma y]
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    MHF Contributor matheagle's Avatar
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    the sum of the expectations OF the n different Y's.
    IS the parameter Y?
    Or are the random variables Y_i
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    y(i) are the random variables
    The distribution of y(i) is Prob(y(i)=t)=p(i)*(1-p(i))^(t-1)

    Thanks for the reply. Looking forward.
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    Member oldguynewstudent's Avatar
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    Quote Originally Posted by himanshubahmani View Post
    What will be the expected value of the sum of geometrically distributed parameter y.

    E [Sigma y]
    You're notation is different than what my book has. But a geometrically distributed variable in my book is a negative binomial distribution and E(X)= \frac{r(1-p)}{p} where r is the number of successes and p is the probability of success.
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    MHF Contributor matheagle's Avatar
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     E\left(\sum_{i=1}^nY_i\right) =  \sum_{i=1}^nE(Y_i)

    where independence is not needed between the Y's.

    SOME geo's start at 0 some start at 1.
    It depends on your definition.
    You might count the first trial or not.
    That r is my n, the number of geo's that you're adding.
    NOTE that if they are indep, then the sum is a neg bio.
    BUT even if they are dependent then the expected value of the sum is still the sum of the expectations.
    Last edited by matheagle; July 7th 2010 at 10:56 PM.
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