ABSTRACT: Is consistency always epistemically virtuous? In this paper, I examine one threat to the traditional view that consistency is a minimum requirement for rational belief. Central to the ...

for \(\sigma >0\) and \(X_0=x\). For any open set \( A \subset \mathbf{R}^d\) assume that you know that \(P(B_t \in A) >0)\) show that the same holds for \(X_t ...

Draw a picture of the region of the \(xy\)-plane were both x and y are between 0 and 1 and \(y \geq x^2\). Find the area of this region ...

In the mathematics entrance exam for Iwate Medical University's School of Medicine, it is important to know how to organize ...

But somewhat surprisingly, the mathematical study of probability began relatively recently, when a troubled gambler reached out to a mathematician for help. [MUSIC PLAYING] Let's start with the word ...