One of the shortcomings of the Poisson distribution is that its variance exactly equals its mean. It is common in practice for the variance of count data to be larger than the mean, so it’s natural to look for a distribution like the Poisson but with larger variance. We start with a Poisson random variable X with mean λ, but then we make λ itself random and suppose that λ comes from a gamma(α, β) distribution. Then the marginal distribution on X is a negative binomial distribution with parameters r = α and p = 1/(β + 1).
The previous post said that the negative binomial is useful because it has more variance than the Poisson. The derivation above explains why the negative binomial should have more variance than the Poisson.
Here are 12 prompts to help you find mathematics-related books for the coming year
oh my gosh: how did I not know about this counting-out system called Yan-Tan...?!— Laura Gibbs (@OnlineCrsLady) November 15, 2019
I was looking up something about the nursery rhyme Hickory Dickory Dock, which some people think is a counting out rhyme, and that led to this British sheep-counting system: https://t.co/NWfJgyicB6 pic.twitter.com/azXjrpo8ob
Ars chats with math teacher Ben Orlin about his book Change Is the Only Constant.
Finally, I decided to build it around all my favorite stories that touched on calculus, stories that get passed around in the faculty lounge, or the things that the professor mentions off-hand during a lecture. I realized that all those little bits of folklore tapped into something that really excited me about calculus. They have a time-tested quality to them where they’ve been told and retold, like an old folk song that has been sharpened over time.
And this is roughly how memory and teaching has always worked. Stories and repetition.
–November 11, 2019 at 09:56AM
Suppose you have a keypad that will unlock a door as soon as it sees a specified sequence of four digits. There’s no “enter” key to mark the end of a four-digit sequence, so the four digits could come at any time, though they have to be sequential. So, for example, if the pass code is 9235, if you started entering 1139235… the lock would open as soon as you enter the 5. How long would it take to attack such a lock by brute force? There are 104 possible 4-digit codes, so you could enter 000000010002…99989999 until the lock opens, but there’s a more efficient way. It’s still brute force, but not quite as brute.
A couple weeks ago I wrote about how De Bruijn sequences can be used to attack locks where there is no “enter” key, i.e. the lock will open once the right symbols have been entered. Here’s a variation on this theme: what about locks that let you press more than one button at a time?
Asking questions in conversation has become problematic. For example, try saying this out loud: “I wonder when Martin Luther King was born?” If you ask that online, a likely response is: “Just Google it!” Maybe with a snarky link: http://lmgtfy.com/?q=when was martin luther king born? https:...
The American Mathematical Society is having their Fall Western meeting here at U. C. Riverside during the weekend of November 9th and 10th, 2019. Joe Moeller and I are organizing a session on App…
Track changes is a popular tool in Word. If you are looking for something similar for LaTeX latexdiff is the answer. For example if you are an academic researcher submitting papers to journals, you…
Preface This is a first draft of a free (as in speech, not as in beer) (although it is free as in beer as well) undergraduate number theory textbook. It was used for Math 319 at Colorado State University – Pueblo in the spring semester of 2014. Thanks are hereby offered to the students in that class — Megan Bissell, Tennille Candelaria, Ariana Carlyle, Michael Degraw, Daniel Fisher, Aaron Griffin, Lindsay Harder, Graham Harper, Helen Huang, Daniel Nichols, and Arika Waldrep — who offered many useful suggestions and found numerous typos. I am also grateful to the students in my Math 242 Introduction to Mathematical Programming class in that same spring semester of 2014 — Stephen Ciruli, Jamen Cox, Graham Harper, Joel Kienitz, Matthew Klamm, Christopher Martin, Corey Sullinger, James Todd, and Shelby Whalen — whose various programming projects produced code that I adapted to make some of the figures and examples in the text.
The author gratefully acknowledges the work An Introductory Course in Elementary Number Theory by Wissam Raji [see www.saylor.org/books/] from which this was initially adapted. Raji's text was released under the Creative Commons CC BY 3.0 license, see creativecommons.org/licenses/by/3.0. This work is instead released under a CC BY-SA 4.0 license, see creativecommons.org/licenses/by-sa/4.0. (The difference is that if you build future works off of this one, you must also release your derivative works with a license that allows further remixes over which you have no control.)
be sure to check out the materials that @poritzj has shared at his website, incl. all you wanted to know about cryptography but were afraid to ask:https://t.co/SdxbbNlNsT
Yet Another Introductory Number Theory Textbook (Cryptology Emphasis Version) — CC-licensed! #Domains19 https://t.co/HsWU5gxvmM
— Laura Gibbs (@OnlineCrsLady) June 10, 2019
No disrespect to "why was six afraid of seven," but "base 10" is the funniest math joke.
Alan Alda wanted to get off the island quickly. Steven Strogatz explains how an 18th century British clergyman could have helped. In this short bonus episode, Steven helps Alan understand something that he’s wondered about for years.
There’s a reasonable basic discussion of Bayesian statistics here.