The random variable X has a semi-circular distribution, with the probability density function (p.d.f) f(x) given by f(x) = { V1 -22 A plot of the p.d.f is given below. -1 0 1 if 1 x 1; otherwise. 1 X (a) Derive the acceptance-rejection method to simulate the random variable X on a computer, by using a uniform random variable between -1 and 1 as the proposal. Assume you have access only to a procedure in the computer that can generate a uniform variable between 0 and 1. (b) What is the expected runtime of the method, in terms of the number of acceptance-rejection/ate trials needed to get one output? Go to Setti