Does anyone know what the expected value of the negative binomial distribution is? Originally I thought it was: r(1p)/p but then I was reading "A first year in prob" by Sheldon and it said that the expected value was r/p. That made more sense because the negative is just like the geometric and the expected value of the geometric is 1/p. B/c the trials are all independent, just r/p made sense. But then I noticed several other books had r(1p)/p. So I began to think maybe it was a typo in Sheldon. But then I saw there was a proof that it was r/p in sheldon. But then I found a website on the internet that also had a proof that it was equal to r(1p)/p. They both looked legitimate. How can this be? Which is the real expected value of the negative binomial? Thanks, John
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Negative binomial
Negative binomial distribution either counts how many times you try until you succeed r times, or how many times you fail until you succeed r times. Two possible approaches to basically the same process, but the resulting means are different.
Yours,
Krzys'Want to know how to pass actuarial exams? Go to: smartURL.it/pass
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Originally posted by krzysioNegative binomial distribution either counts how many times you try until you succeed r times, or how many times you fail until you succeed r times. Two possible approaches to basically the same process, but the resulting means are different.
Yours,
Krzys'
For the first case you mention :
x is the total times you try until you succeed r times, the expected value will be r/p, (note, here the possible value for x is r, r+1, r+2 ... )
the second case:
x is the times you fail until you succeed r times, the expected value will be r(1p)/p
(note, here the possible value for x is 0, 1, 2,...)
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Originally posted by leerobb1966 View PostHi,
I read in two sources that the mean of Geometric Distribution is the reciprocal of the success rate, e.g. 1/p.
But I also read in some solution that the the mean as 1p/p.
Which one is right?
Thanks for help.
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Originally posted by NoMoreExams View PostYou will benefit from reading this: http://en.wikipedia.org/wiki/Geometric_distribution and also using parantheses where appropriate. "1p/p" means 1(p/p) = 11 = 0", you obv. meant (1p)/p
and I will be more careful with expressions.:tongue:My name is Yuchin.
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