A colleague recently asked "why should the average get closer to the mean when we increase the sample size?" We should interpret this question as asking why the standard error of the mean gets smaller as n increases. The central limit theorem shows t...

The Monty Hall problem illustrates a simple setting where intuition often leads to a solution different from formal reasoning. The situation is based on the game show Let's Make a Deal. First, Monty puts a prize behind one of three doors. Then the player chooses a door. Next, (without moving ...

Suppose we wanted to assess the probability P(X=x) for a binomial random variate with n = 10 and with p = .81, .84, ..., .99. This could be helpful, for example, in various game settings. In SAS, we find the probability that X=x using differences in t...