ECONOMIC QUESTIONS:

You are given a stream of standard identically and independently distributed uniform [0,1] random variables U1, U2, Uj, . ... Describe how to use this random variable stream to generate random variates with the following distributions: (i) The discrete distribution with possible values A, B and C with respective probabilities 1/5, 1/4 and 11/20. [2] (ii) The continuous distribution with probability density function f(x)=(10-x)/18 for 40; is a continuous-time martingale. [4] (iii) Let T = inf(t : S(t) = a} for some 0 last-> co. (b) Deduce that P[T 1 and define T, as before. (a) Explain why E[S(T.)] = aPIT,