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 Post subject: Xi~B(n, p) Yj~B(m, p) Xi+Yj~B(n+m, p)Posted: Tue, 17 Jul 2012 06:06:21 UTC

Joined: Sun, 27 May 2012 16:48:31 UTC
Posts: 8
Where can I find out (the prove of)this topic?

Xi has binomial distribution B(n, p)
Yj has binomial distribution B(m, p)

Xi+Yj has binomial distribution B(n+m, p)

P()
P()

P()

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 Post subject: Re: Xi~B(n, p) Yj~B(m, p) Xi+Yj~B(n+m, p)Posted: Tue, 17 Jul 2012 06:09:32 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
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Location: Austin, TX
BookInquiry wrote:
Where can I find out (the prove of)this topic?

Xi has binomial distribution B(n, p)
Yj has binomial distribution B(m, p)

Xi+Yj has binomial distribution B(n+m, p)

P()
P()

P()

Just use the cdf function.

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 Post subject: Re: Xi~B(n, p) Yj~B(m, p) Xi+Yj~B(n+m, p)Posted: Tue, 17 Jul 2012 06:58:47 UTC
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Just use the cdf function.

... assuming independence!

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 Post subject: Re: Xi~B(n, p) Yj~B(m, p) Xi+Yj~B(n+m, p)Posted: Tue, 17 Jul 2012 07:00:08 UTC
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outermeasure wrote:
Just use the cdf function.

... assuming independence!

Yes, of course. I really should have said that. X(

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 Post subject: Re: Xi~B(n, p) Yj~B(m, p) Xi+Yj~B(n+m, p)Posted: Wed, 18 Jul 2012 07:28:01 UTC

Joined: Sun, 27 May 2012 16:48:31 UTC
Posts: 8
Yeah... random variables are assumed to be independent.
I don't even know the start of these proofs.
Any books/ internet materials should I refer to?

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 Post subject: Re: Xi~B(n, p) Yj~B(m, p) Xi+Yj~B(n+m, p)Posted: Wed, 18 Jul 2012 13:44:16 UTC
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BookInquiry wrote:
Yeah... random variables are assumed to be independent.
I don't even know the start of these proofs.
Any books/ internet materials should I refer to?

Just compute the probability mass function.

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 Post subject: Re: Xi~B(n, p) Yj~B(m, p) Xi+Yj~B(n+m, p)Posted: Wed, 18 Jul 2012 18:52:02 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12103
Location: Austin, TX
BookInquiry wrote:
Yeah... random variables are assumed to be independent.
I don't even know the start of these proofs.
Any books/ internet materials should I refer to?

Have you ever seen a "what is the distribution of the sum of these two random variables" problem before? They almost invariably go the same way each time where you do convolution to get the distribution of the sum. If you're having issues with this, check out this basic primer link.

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 Post subject: Re: Xi~B(n, p) Yj~B(m, p) Xi+Yj~B(n+m, p)Posted: Fri, 20 Jul 2012 03:10:43 UTC

Joined: Sun, 27 May 2012 16:48:31 UTC
Posts: 8
Have you ever seen a "what is the distribution of the sum of these two random variables" problem before? They almost invariably go the same way each time where you do convolution to get the distribution of the sum. If you're having issues with this, check out this basic primer link.

I come across with joint probability distribution problems in this book: Advanced Mathematics 2 Perkins
It mentions the conclusions above without proofs.
I have no experience in these problems.

I don't even get the idea about it. Prerequisites are necessary?

I just learnt several distributions: Binomial, geometric, poison, normal,
I am expecting: sample distribution, joint probability distribution(linear/ non-linear combination of two or three sets of random variables), negative Binomial distribution... but I don't know about which references materials(books or internet) best learn about thee topics.

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 Post subject: Re: Xi~B(n, p) Yj~B(m, p) Xi+Yj~B(n+m, p)Posted: Fri, 20 Jul 2012 11:04:42 UTC
 Moderator

Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12103
Location: Austin, TX
BookInquiry wrote:
Have you ever seen a "what is the distribution of the sum of these two random variables" problem before? They almost invariably go the same way each time where you do convolution to get the distribution of the sum. If you're having issues with this, check out this basic primer link.

I come across with joint probability distribution problems in this book: Advanced Mathematics 2 Perkins
It mentions the conclusions above without proofs.
I have no experience in these problems.

I don't even get the idea about it. Prerequisites are necessary?

I just learnt several distributions: Binomial, geometric, poison, normal,
I am expecting: sample distribution, joint probability distribution(linear/ non-linear combination of two or three sets of random variables), negative Binomial distribution... but I don't know about which references materials(books or internet) best learn about thee topics.

I learned about the basic distributions from Sheldon Ross' basic book on the subject (he also has a more advanced one, which is certainly not appropriate if you have never seen convolution before).

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