Question: Suppose Y,,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 (ii)

Suppose Y,,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 (ii) n = 1,000.

b. Suppose c is a positive number. Show that Pr(10-csys 10+

c) becomes close to 1.0 as a grows large.

c. Use your answer in

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

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