6.14 Suppose we were not supplied with the Matlab routine randn for simulating normal random variables. A simple way to simulate approximately standard normal random variables is to make use of the Central Limit Theorem of probability theory, and set Y = 

12 i=1 Ui − 6, where the {Ui} are independent, identically distributed U(0, 1) random variables. For example, in Matlab one might set Y = sum (rand(12, 1)) - 6.

Use this approximation for the remainder of this question.

(i) Decide on the parameters of a mixture of two normal pdfs.

(ii) Simulate a sample of size 50 from this mixture.