Wikipedia:Reference desk/Archives/Mathematics/2016 September 4

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September 4

Translation of Bourbaki to English

Bourbaki's Algebra chapters 1–3 and 4–7 have been translated to English. Were the remaining chapters translated (most particularly N. Bourbaki, Formes Sesquilinéaires et Quadratiques)? —Quondum 01:29, 4 September 2016 (UTC)

Binomial distribution

The probability that n experiments have k successes, when the success probability is p,

$P_{k}={\binom {n}{k}}p^{k}(1-p)^{n-k}$

satisfies the formula

${P_{k+1} \over P_{k}}={n-k \over k+1}{p \over 1-p}$

I wonder how the latter formula can be proved without reference to the former formula?

Bo Jacoby (talk) 18:01, 4 September 2016 (UTC).

I have not gone through the details, but it seems promising to me to use the simple (i.e. obvious) rule of recursion

$P_{n,k}=p\cdot P_{n-1,k-1}+(1-p)\cdot P_{n-1,k}$

plus suitable boundary conditions, and then use your formula with induction. By "boundary conditions", I am referring to the cases $k=0$ and $k=n$, which must be proved separately. —Quondum 21:19, 4 September 2016 (UTC)