Introduction to Econometrics 3rd Edition by James Stock, James Stock

Exercise 15

Suppose that Y₁ , Y₂ ,..., Y n are random variables with a common mean y , a common variance and the same correlation (so that the correlation between Y i and Y j is equal to for all pairs i and j, where i j ).
a. Show that
b. Suppose that n = 2. Show that and
c. For n 2, show that and
d. When n is very large, show that