Let N ~ Poisson with mean mu.
Let X|N=n ~ Binomial(n,p).

Show that X ~ Poisson with mean p*mu.

source: STAT560 - Assignment 2, Problem 2

What most people call a "formal" proof (and what appears in the solution linked) involves writing down the relevant pdfs and working out infinite sums.

I prefer to prove this by simple intuitive logic:( Read more... )

Last week, I had an excellent chat with Terry Stewart over AIM. We covered:
* cognitive modeling
* "neural compilers"
* philosophy of science (empirical vs theoretical models in physics and cogsci, unification/integration, predictions vs explanations, reduction). See his excellent paper here ( Read more... )

I just found out that there is a journal about Hybrid Intelligent Systems, i.e. systems that use multiple representations, multiple methodologies, etc. It reminds me of Minsky's speech about multiple representations being important, which I very much agree with ( Read more... )

Zeilberger on two pedagogical principles, via rweba

<< The first one, due to my colleague and hero Israel Gelfand, I will call the Gelfand Principle, which asserts that whenever you state a new concept, definition, or theorem, (and better still, right before you do) give the SIMPLEST possible non-trivial example. For example, suppose you want to teach ( Read more... )

Jeremy Avigad's "Mathematical Method and Proof" exposes lots of the ideas that I've been writing about time and time again on this blog, under the tags formal_math and formal_ed (for my education-related formal dreams / practical epistemology ( Read more... )

I should read Freek's notes again sometime.

Gustavo Lacerda - A QED Project for Science: The Promises of Computer-Level Formalization

Please comment, argue, criticize!

How crackpotty does it sound? Where does it need to improve in order to meet journal standards?

Pralam: A Practical Language for Mathematics
I'm proposing an easy way of formalizing mathematics, by translating mathematical statements into FOL formulas. Please comment or contribute on the wiki.

I wish I had written this:
Manfred Kerber, Martin Polleti - On the Design of Mathematical Concepts

That foundational systems like first-order logic or set theory can be used to construct large parts of existing mathematics and formal reasoning is one of the deep mathematical insights. Unfortunately it has been used in the field of automated ( Read more... )

It's impossible to prove Pi_1 statements without axioms that talk about infinity ( Read more... )