query: Showing a relation between binomial and negative binomial analytically
positive_passages.docid: 20009
positive_passages.text: Relationship between binomial and negative binomial distributions (how to extend the probability space?)
negative_passages.docid: 4855
negative_passages.text: How to show that this binomial sum satisfies the Fibonacci relation?
negative_passages.docid: 4931
negative_passages.text: variation of the binomial theorem
negative_passages.docid: 58972
negative_passages.text: Proof/Derivation of Closed form of Binomial Expression $\sum\limits_{k=0}^{2n}(-1)^k\binom{2n}{k}^2$
negative_passages.docid: 15666
negative_passages.text: explanation for a combinatorial identity involving the binomial coefficient
negative_passages.docid: 146810
negative_passages.text: How to derive this binomial identity?
negative_passages.docid: 31196
negative_passages.text: Prove $\binom{n}{a}\binom{n-a}{b-a} = \binom{n}{b}\binom{b}{a}$
negative_passages.docid: 64319
negative_passages.text: Deriving the canonical link for a binomial distribution
negative_passages.docid: 94784
negative_passages.text: $\sum_{k=-m}^{n} \binom{m+k}{r} \binom{n-k}{s} =\binom{m+n+1}{r+s+1}$ using Counting argument
negative_passages.docid: 65335
negative_passages.text: A "binomial" generalization of harmonic numbers
negative_passages.docid: 40784
negative_passages.text: $\sum_{k=m}^{n}(-1)^k\binom{n}{k}\binom{k}{m}=0, n>m\geq 0$
negative_passages.docid: 122786
negative_passages.text: C: The Math Behind Negatives and Remainder
negative_passages.docid: 146762
negative_passages.text: Closed form for $\sum_{k=0}^{n} \binom{n}{k}\frac{(-1)^k}{(k+1)^2}$
negative_passages.docid: 28936
negative_passages.text: Proving equation with binomial coefficient
negative_passages.docid: 128856
negative_passages.text: Show the result of the following infinite sum, based on a binomial random variable conditioned on a Poisson random variable
negative_passages.docid: 49783
negative_passages.text: A possible inequality related to binomial theorem (or, convex/concave functions)
negative_passages.docid: 82534
negative_passages.text: What is the difference and relationship between the binomial and Bernoulli distributions?