Question: 1. Problem 11.11 Let (X,Y) be a point chosen at random inside the unit circle. Define V and W by V = X 2ln(Q)/Q and

1. Problem 11.11 Let (X,Y) be a point chosen at random inside the unit circle.

Define V and W by V = X√

−2ln(Q)/Q and W = Y√

−2ln(Q)/Q, where Q =X2+Y2.Verifythat the random variables V and W are independent and N(0,1) distributed. This method for generating normal variates is known as Marsaglia’s polar method.

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