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

Exercise 31

Suppose Y i ,i = 1,2,..., n, are i.i.d. random variables, each distributed N (10,4).
a. Compute Pr(9.6
10.4) when (i) n = 20, (ii) n = 100, and (iii) n = 1,000.
b. Suppose c is a positive number. Show that Pr(10 - c
10 + c) becomes close to 1.0 as n grows large.
c. Use your answer in (b) to argue that
converges in probability to 10.