Fall 2011 Homework 5: Question 4
Let $F$ be a CDF which is continuous and strictly increasing. The inverse function, $F^{-1}$, is known as the quantile function, and has many applications in statistics and econometrics. Find the area under the curve of the quantile function from 0 to 1, in terms of the mean $\mu$ of the distribution $F^{-1}$. Hint: Universality.
Solution: (a) The integral is of the inverse of F of u from 0 to 1 is μ.
"Mathematics is the logic of certainty, but statistics is the logic of uncertainty."