Fall 2011 Strategic Practice 9: Section 2 (Order Statistics) - Question 1
Let be i.i.d. Unif(0, 1). Find the PDF of the jth order statistic (including the normalizing constant), and its mean and variance.

Solution:
U(j) ~ Beta(j, n − j + 1). Mean u = j / n+1. Variance u(1-u) / n+2.

"Mathematics is the logic of certainty, butstatistics is the logic of uncertainty."