Supplementary
Reading
Heads or Tails
A translation into English of the article “Croix ou Pile” by Jean le Rond d’Alembert. The article originally appeared in the Encyclopedia, or a Systematic Dictionary of the Sciences, Arts, and Crafts in the second half of the 18th century. The translation was produced by R. Pulskamp of Xavier University but is no longer available on the university website.
On Moment-Generating Functions
A discussion of the formula for the moment-generating function, featuring the "discrete dominated convergence theorem."
Properties of the Correlation Coefficient
It is shown how a vector space structure on the set of random variables helps to establish a basic property of the correlation coefficient. Along the way, an interesting application of Chebyshev’s inequality shows that positive random variables with zero expectation must be identically zero.
