I'll begin with a familiar image:That plot shows the closing values of the S&P 500 index from 1990 until today. It's a useful representation -- at a glance, you can tell when the market rose and fell. That said, it does have some problems: we're...

You, the player, must think of some set, eg "odd numbers" or "perfect squares," and that'll be your little secret. Now think of some numbers that live in the intersection of your set and the integers {1, 2, ... , 100} -- for example, if you've chosen ...

For some reason I feel like plotting some random walks. Nothing groundbreaking, but hopefully this post will be useful to someone. Here's my R code:# Generate k random walks across time {0, 1, ... , T}T <- 100k <- 250initial.value <- 10GetRa...

A few days ago I heard a talk about Simpson's paradox, and I decided to write a little example in R:library(MASS) # For multivariate normals# List of (vectors of) meansmu <- list(c(5, 175), c(6.25, 110))# List of covariance matricessigma ...

Suppose N people (and their hats) attend a party (in the 1950s). For fun, the guests mix their hats in a pile at the center of the room, and each person picks a hat uniformly at random. What is the probability that nobody ends up with their own hat?E...

Earlier today I read a post about truncated normals, and one plot in particular jumped out at me:By definition, the truncated normal should have zero density everywhere to the left of the truncation point, but that's not what we see in the plot. What'...

Suppose you have 10 objects from which you take a sample of size 20 (with replacement, or you're in trouble). What's the probability that each object was chosen at least once? Getting an answer via simulation is pleasantly easy:f <- function(n=10,...

In everyday life I hear the word "correlation" thrown around far more often than "dependence." What's the difference? Correlation, in its most common form, is a measure of linear dependence; the catch is that not all dependencies are linear. The set...

Today I made the mistake of clicking on the "Next Blog" button, which took me to a rather inane post complaining that crows are (obviously) stupid (because they are sometimes hit by cars). I was reminded that crows are actually quite smart.