My Math Forum Problem with expected value in Geometric distribution

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November 6th, 2016, 02:32 PM   #1
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Problem with expected value in Geometric distribution

Hello,
Could you explain red line in the below image?
What we used derivative?
Thanks
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 November 6th, 2016, 04:12 PM #2 Senior Member     Joined: Sep 2015 From: CA Posts: 933 Thanks: 504 what exactly don't you understand? can you recognize that $-\dfrac{d}{dp}(1-p)^n = n(1-p)^{n-1}$ ? Thanks from life24
November 6th, 2016, 10:32 PM   #3
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Quote:
 Originally Posted by romsek what exactly don't you understand? can you recognize that $-\dfrac{d}{dp}(1-p)^n = n(1-p)^{n-1}$ ?
Thank you,
Negative come from?
And why in first summation start from 1 then became 0 ?

November 6th, 2016, 10:34 PM   #4
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Quote:
 Originally Posted by life24 Thank you, Negative come from?
the $-p$ in $(1-p)$

It really should have been 0 all along but since there was a factor of $n$ in the earlier expressions the 0th term was 0 and was left out.

Last edited by romsek; November 6th, 2016 at 10:36 PM.

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