Feige’s conjecture
Let $X_1, X_2, \dots, X_n$ be independent random variables, each with mean at most 1. We want to maximise the probability that their sum $S = \sum_{i=1}^n X_i$ is at least $n + \delta$ for some $\delta > 0$. How do we do this?
Matthew Aldridge
The website of Dr Matthew Aldridge, Lecturer in Statistics at the University of Leeds
Latest posts
Some of my favourite things American
“A Change Is Gonna Come” “A Perfect Day for Bananafish” the Apollo program Barbara Stanwyck Bob Dylan Calvin Trillin Claude Shannon and information theory Different Trains Do The Right Thing Dwight Garner’s book reviews Edward Hopper’s Nighthawks eggs Benedict Ernest Hemingway’s novels and short stories Francis Ford Coppola’s run of films in the 1970s The Great Gatsby hip-hop heavier-than-air…
A (more) probabilistic proof of a geometric result
Here’s a cute little paper: it’s called “Generalization of Marion’s theorem: volumes of central polytopes obtained by trisecting the edges of simplices” by Yu. V. Kazakov.
Guardian 100 best novels (stats and errors)
I have been enjoying reading through (and arguing with!) the Guardian’s 100 best novels list . You can see the whole top 100 at that link, but the top 10 is this: Middlemarch by George Eliot Beloved by Toni Morrison Ulysses by James Joyce To the Lighthouse by Virginia Woolf In Search of Lost Time by Marcel Proust Anna Karenina by Leo Tolstoy War and Peace by Leo Tolstoy Jane Eyre by Charlotte…
The multiset coefficient deserves more respect!
Being the second in a series of blogposts quite unnecessarily scolding the reader about the binomial coefficient (Previously: “Don’t write the binomial coefficient as n! / k! (n-k)!”)
4 is discrete π
Recap
2 is discrete e
Here’s a question that came into my mind as I was falling asleep last night: What’s the discrete equivalent of the exponential function $\exp(x) = \mathrm{e}^x$?
Don’t write the binomial coefficient as n! / k! (n-k)!
The binomial coefficient $\binom{n}{k}$, pronounced “$n$ choose $k$”, is the number of ways of choosing a collection of $k$ objects from a set of $n$ objects.
The geometric distribution starts from 0
You keep rolling a dice until you get a six: how many rolls does this take?
Photos: Belfast
Belfast and the northern coast of Northern Ireland, 3–6 August 2025