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I'm given a set of random variables where each $X_i$ has distribution:

$p(x_i;\theta) = \theta(1-\theta)^{x_i}$ for $x=0,1,2,...$

I need to compute the expectation $E(\sum_{i=1}^n X_i)$.

Is the distribution of $X_i$ something known?

I cannot recognize as a well known distribution.

Thanks in advance.

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  • 2
    $\begingroup$ Geometric distribution. $\endgroup$ – Monolite Apr 15 '18 at 20:16
  • $\begingroup$ Great, thanks. I guess that is a very well known distribution simply out of my current knowledge and experience. Thanks for your comment!. I just checked out the wikipedia page for Geometrical distribution and matches perfectly when the support is $x=0,1,2,3,...$ as in my case. Thanks again. Now just need to figure out the distribution of the summation of $n$ geometric random variables. $\endgroup$ – pkenneth81 Apr 15 '18 at 20:24
  • $\begingroup$ see here $\endgroup$ – thesmallprint Apr 15 '18 at 20:28

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