Use the result of Exercise 6.3-10.

(a) Find the joint pdf of Y1 and Yn, the first and the nth order statistics of a random sample of size n from the U(0, 1) distribution.

(b) Find the joint and the marginal pdfs of W1 = Y1/Yn and W2 = Yn.

(c) Are W1 and W2 independent?

(d) Use simulation to confirm your theoretical results.

Reference Exercise 6.3-10

Use the heuristic argument to show that the joint pdf of the two order statistics Yi < Yj is

Chapter 3 & 12 4/20/2017 in-class notes Chapter 3: measures of linear association between two quantitative variables (covariance and correlation coefficient) Correlation Changes (increase/decrease) in values of variables x are associated with (are accompanied by) changes in the values of y (and vice versa) Often we are interested...