The mean of means (of state e) is close to .36. If you take .3 * .36 + .4 * (1-.36), you get .364, so this seems to make sense. Note that I’m weighting the switching to e percentage based on the percentage of being in that state in the first place.
The Monty Hall Problem is famous in the world of statistics and probability. For those struggling with the intuition, simulating the problem is a great way to get at the answer. Randomly choose a door for the prize, randomly choose a door for the user to pick first, play out Monty’s role as host, and then show the results of both strategies.
The numeric output will vary, but look something like:
Clustering is a useful technique for exploring your data. It groups records into clusters based on similar features. It’s also a key technique of unsupervised learning. The following is a simple example in R where I plotted the clusters and centroids.
The example uses the mtcars dataset built into R, which contains auto data extracted from Motor Trend Magazine in 1973-1974.
Clustering is done with the kmeans() function. Note that the graph is 2-dimensional, and I cluster by 2 features, but you could cluster by more features and project down to a 2-dimensional plane.