In this blog article, Allen Downey shows that marathon world record times have been advancing at a linear rate. He uses least squares estimation to calculate the parameters of the line of best fit, and predicts that the first 2-hour marathon will occur around 2041.

I extend his model, and calculate how likely it will be that someone will run a 2-hour marathon in 2041. Or more generally, I find the probability distribution of a certain record being hit on a certain date.