2,915 karma · joined August 31, 2015
https://www.dam.brown.edu/people/mumford/beyond/papers/2000b...
Please correct me if I'm wrong. I want to learn.
https://www.weather-us.com/en/california-usa/san-diego-clima...
1, 5, 11, 19, 29, 41, 55, 71, 89, ...
Searching it on the OEIS (a great resource for mathematics) gave
http://oeis.org/search?q=1%2C5%2C+11%2C+19%2C+29%2C+41%2C+55...
It turns out that these are precisely the first values of the Fibonacci polynomial n^2 - n - 1
I haven't verified this fact, but it seems like it comes from an application of the generating function of the Fibonacci numbers.
I posted my code in another comment
11/89 should be 11/8900
This can be verified by using the following Sage code (simply go to https://sagecell.sagemath.org/ to avoid installing sage)
b = 10
A = Matrix([[0, 1],[1/(b**2), 1/b]])
I = matrix.identity(2)
show((I - A).inverse() * Matrix([[1/b**2],[1/b**3]]))https://en.wikipedia.org/wiki/Copula_(probability_theory)#Sk...
I think this is a nice article, but I can't help but be frustrated by the stochasticity of HN since I posted it yesterday :D
It's meant for a second course in linear algebra and the focus is on abstract vector spaces and linear transformations (rather than a table of numbers perspective). It also doesn't use determinants until the last chapter.
This may be pedantic, but an object that determines a distribution that isn't based on expected values is the CDF. In my first probability course in undergrad I think we defined probability mass functions and probability density functions first and defined CDFs in terms of them, but from a measure theoretic point of view, the CDF is more fundamental since it is defined for continuous and discrete distributions (and also for distributions that are neither).
There's another interpretation of the mean (and conditional expectation) as quantities minimizing squared error. It's not surprising that squared error and variance are so similar and that these are connected.
I'm not so sold on the idea that a match system will improve labor liquidity. How do you negotiate wages? Medical residents are stuck with the salary of the site that they matched at. When you enter the match, you cannot simply choose not to accept the job "offer" you are given.
Can a biologist fix a radio?--Or, what I learned while studying apoptosis. https://www.ncbi.nlm.nih.gov/pubmed/12242150