Let be a CDF which is continuous and strictly increasing. The inverse function, , 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 of the distribution . 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, butstatistics is the logic of uncertainty."