## maximized entropy of a finite distribution

I received the following tweet yesterday from @ProbFact and decided to check it out in more detail: Two-Dimensional Case I generated the following test to investigate the claim: Create four category discrete distributions where two of the categories have 0.25 probability each, and the third category probability varies between 0.1 and 0.4. The fourth category’s […]

## simulating the Monty Hall puzzle

The Monty Hall puzzle (named after the original host of Lets Make a Deal) offers contestants three identical doors. One of these doors leads to the contestant winning a new car, while the other two lead to rooms containing goats. The contestant selects a door, and the host immediately opens up one of the two […]

## pondering Chebyshev’s inequality

Chebyshev’s inequality states that the probability that a random variable falls within k standard deviations of the mean of a probability distribution is at least Checking this out in R for an arbitrary gamma distribution yields: We can compare the two areas by first plotting the area under the gamma curve within k standard deviations […]

## simulated confidence intervals

In my last post, I demonstrated how repeated sampling from any probability distribution produces a normally-distributed distribution of the sample means, given a sufficiently large sample size. Here I describe how to use this distribution of sample means to define a confidence interval around the mean of any given sample, and simulate production of such […]