What does $dF(y)$ mean?
Sorry for the silly question. To put it into context. I am trying to figure out how to do solve this problem but I'm not sure how and I think my understanding of notation might be stopping me. Also, if anyone knows the step to solve this I would also appreciate that.
$$ 0 = ( 1 – \tau ) \int _ { – \infty } ^ { \hat { x } } d F ( x ) – \tau \int _ { \hat { x } } ^ { \infty } d F ( x ) = F ( \hat { x } ) – \tau $$
Best Answer
Since this involves Probability Theory I assume that $F$ is a distribution funciton. There is a unique probability measure $\mu$ on the Borel sets of $\mathbb R$ such that $\mu (-\infty,x]=F(x)$ for all $x$ and the notation $\int h(x)dF(x)$ stands for $\int hd\mu$.