Source: Thunder Bay, Canada. Used with permission of Dan Hunt, MD. Coincidences attract our attention because they seem weird, odd, or unlikely. Their improbability stimulates wonder—“what are the ...

Let $(X, \mathscr{A}, P)$ be a probability space and $\mathscr{B}$ a sub-$\sigma$-algebra of $\mathscr{A}$. Some results on regular conditional probabilities given $\mathscr{B}$ are proved. Using ...

This article provides a completion to theories of information based on entropy, resolving a longstanding question in its axiomatization as proposed by Shannon and pursued by Jaynes. We show that ...