According to the central limit theorem, if random variables, , are independent and identically distributed, is sufficiently large, then the distribution of their sample mean, , is approximately normal, and this approximation is better as increases. One of the most remarkable aspects of the central limit theorem (CLT) is its validity for any parent distribution of […]
Another X’mas Le Monde mathematical puzzle: A regular dice takes the values 4, 8 and 2 on three adjacent faces. Summit values are defined by the product of the three connected faces, e.g., 64 for the above. What values do the three other faces take if the sum of the eight summit values is 1768? […]
Introduction I saw an interesting problem that requires Bayes’ Theorem and some simple R programming while reading a bioinformatics textbook. I will discuss the math behind solving this problem in detail, and I will illustrate some very useful plotting functions to generate a plot from R that visualizes the solution effectively. The Problem The following question is […]
I’ve been showing my new favourite toys to just about anyone foolish enough to actually engage me in conversation. I described how my shiny new set of non-transitive dice work here, complete with a map showing all the relevant probabilities. All was neat and tidy and wonderful until fellow ecologist, Aaron Ball, tried to burst […]
I’ve been showing my new favourite toys to just about anyone foolish enough to actually engage me in conversation. I described how my shiny new set of non-transitive dice work here, complete with a map showing all the relevant probabilities. All was neat and tidy and wonderful until fellow ecologist, Aaron Ball, tried to burst [...]
A very special package that I am rather excited about arrived in the mail recently. The package contained a set of 6-sided dice. These dice, however, don’t have the standard numbers one to six on their faces. Instead, they have assorted numbers between zero and nine. Here’s the exact configuration: Aside from maybe making for […]
