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Math Help - Can anyone do this proof?

  1. #1
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    Can anyone do this proof?

    Let X denote a Geometric random variable with probability of success p. Show that the

    sum of probabilities of all possible outcomes of X is 1.



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  2. #2
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    Re: Can anyone do this proof?

    Quote Originally Posted by MathJack View Post
    Let X denote a Geometric random variable with probability of success p. Show that the

    sum of probabilities of all possible outcomes of X is 1.

    Note that 0\leq p \leq1.

     \sum^{\infty}_{k=1}P(X=k) = \sum^{\infty}_{k=1}p(1-p)^{k-1} = p \sum^{\infty}_{k=1}(1-p)^{k-1} =  p\left(\dfrac{1}{1-(1-p)}\right)=\dfrac{p}{p}=1
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