All Questions
Tagged with formal-proof elementary-proofs
2 questions
5
votes
4
answers
1k
views
Binomial ID $\sum_{k=m}^p(-1)^{k+m}\binom{k}{m}\binom{n+p+1}{n+k+1}=\binom{n+p-m}{n}$
Could I get some help with proving this identity?
$$\sum_{k=m}^p(-1)^{k+m}\binom{k}{m}\binom{n+p+1}{n+k+1}=\binom{n+p-m}{n}.$$
It has been checked in Matlab for various small $n,m$ and $p$. I have a ...
- 573
1
vote
0
answers
259
views
How to prove this Gaussian Mixture theorem? (Fitting/Overfitting)
Note from OP: I gave up and reposted this Question with a Bounty on Cross Validated HERE.
In certain applications, we approximate an unknown pdf by placing uniformly weighted Gaussian terms at each ...
- 111