2.15 Suppose Yi, i = 1, 2,

c, n, are i.i.d. random variables, each distributed N(10, 4).

a. Compute Pr(9.6 … Y … 10.4) when (i) n = 20, (ii) n = 100, and

(iii) n = 1000.

b. Suppose c is a positive number. Show that Pr(10 - c … Y … 10 + c)

becomes close to 1.0 as n grows large.

c. Use your answer in

(b) to argue that Y converges in probability to 10.