Answer Happy

3. A research has been done to find the best-fitted distribution to a set of indi- vidual claim data. The result suggests a distribution whose density is given by 0. y <0, fy(y) = 1600 20ye + { -10y (y +10)3' y > 0. (a) Use the linear congruential generator Xi+1 = (aX, + c) mod m, to generate 3 standard uniform random variables U, U, and U3 (round- ing to 3 decimal places). Here a = 100, c = 123,456, m = 1, 111, 111 and X, is chosen as the last 5 digits of your student ID number (i.e. 2014XXXXX). [3 marks) (b) Construct an algorithm to simulate random numbers drawn from the density function fy(y). (Hint: you might need to use g(y) = 9e9y in the acceptance-rejection method.] [6 marks (c) Use simulated numbers Uı, U, and Uz from part (a) and the algorithm from part (b) to generate a sample drawn from the density function fy(y). [4 marks]