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PMF and MGF of this problem

nacho

Active member
Sep 10, 2013
156
is part a) simply the sum of the PMFs of the poisson and exponential random variables we are given?

I can't quite make sense of this question. Where it says "identify a distribution..."
is it looking for us to say something like a gamma random variable or a geometric random variable etc?

thank you!
 

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chisigma

Well-known member
Feb 13, 2012
1,704
is part a) simply the sum of the PMFs of the poisson and exponential random variables we are given?

I can't quite make sense of this question. Where it says "identify a distribution..."
is it looking for us to say something like a gamma random variable or a geometric random variable etc?

thank you!
The statement of the problem is not clear at 100 x 100, but what I undestand is the PMF and MGF of the number N of customers arriving in a time T. N is Poisson distributed so that the PMF is...


$\displaystyle P \{ N = n \} = \frac{(\beta\ T)^{n}}{n!}\ e^{- \beta\ T}\ (1)$


... and the MGF is...


$\displaystyle E \{ e^{N\ t}\} = \sum_{n=0}^{\infty} P \{N = n\}\ e^{n\ t} = e^{\beta\ T\ (e^t-1)}\ (2)$

Kind regards

$\chi$ $\sigma$
 

nacho

Active member
Sep 10, 2013
156
chisigma, a million thank yous are not enough to express my gratitude for you.

someone make this man a mod, he is legendary.

i am also happy that you also thought the question wasn't clear, that gives me some confidence :)

Thanks again, this is enough to get me started on the rest !
 

chisigma

Well-known member
Feb 13, 2012
1,704
... someone make this man a mod, he is legendary...
Thank for Your compliments!... regarding the 'moderation' I consider myself totally unable to cover the role of moderator because I think that, in a family of people with the ideal to promote the mathematical knowledge, the figure of moderator shouldn't be necessary. For that reason I prefer to remain 'site helper' and to continue to do my best possible to MHB...

Kind regards

$\chi$ $\sigma$