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« Every other number is negative »

I don't understand this part. Other than what? Is there a translation error or something?

PS. Ok, got it. http://dictionary.reference.com/browse/every%20other

"Every other" is an english idiom to indicate alternation. I did not know it.

No error, it means every other coefficient in the p.g.f. is negative, which is like saying that certain outcomes have negative probability. In the p.g.f. for the double coin example, the coefficient of the monomial for z^0 is 1/4, meaning that the probability of two coins flipping to both tails is 1/4. If the coefficient were negative there, it doesn't make sense intuitively but that's the "magic" when it comes to these magical half coins.

I'm sorry I was not clear. It's not the negative part I don't get, it's the "every other number". Other than what? I'm not an english native speaker so it might be a math-related english expression I don't know. Is it?

"every other number" == "every second number", i.e. the first, third, fifth ... coefficients are positive, while the second, fourth, sixth .. coefficients are negative. Hope this helps.

"every other X" usually means, every even or every odd X, like:

... 0 1 0 2 0 3 0 4 0 5 ...

Every other number is 0 above.

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