Timeline for The sum of two independent variables following the Binomial Distributions
Current License: CC BY-SA 4.0
8 events
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| Jul 16, 2018 at 17:47 | comment | added | kirma |
For instance, look at MultinomialDistribution documentation. Single value distributions work with single variable, others demand list of correct length... but you can't trivially combine them.
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| Jul 16, 2018 at 17:01 | comment | added | MarcoB | @kirma I don't understand your point. Could you elaborate on your second sentence? | |
| Jul 16, 2018 at 16:12 | comment | added | kirma |
{x1, x2} \[Distributed] ... would be fine with multinomial distributions. The form of Distributed must follow each distribution individually, though.
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| Jul 16, 2018 at 16:09 | comment | added | MarcoB |
@Bob Both are excellent points, thank you. I added the result of evaluation of TransformedDistribution as it is indeed more readable, and fixed the output image, which I had copied wrong.
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| Jul 16, 2018 at 16:08 | history | edited | MarcoB | CC BY-SA 4.0 |
Fixed typo in result, added comment from Bob Hanlon
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| Jul 16, 2018 at 15:17 | comment | added | Bob Hanlon |
Evaluation of just TransformedDistribution[ x1 + x2, {x1 \[Distributed] BinomialDistribution[n, p], x2 \[Distributed] BinomialDistribution[n, p]}] gives BinomialDistribution[2 n, p] which makes it clear that the result is a BinomialDistribution rather than having to visually recognize the fact from the PDF. And on my system, your input evaluates to Piecewise[{{(1 - p)^(2*n - y)*p^y* Binomial[2*n, y], 0 <= y <= 2*n}}, 0]
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| Jul 16, 2018 at 14:56 | vote | accept | user120911 | ||
| Jul 16, 2018 at 14:53 | history | answered | MarcoB | CC BY-SA 4.0 |