You are given the following eight random number generators:

(i) The linear congruential method with 0 5, 5, 1, 16. x a c m

(ii) The multiplicative congruential method with 5 0 1, 5, 2 . x a m = = =

(iii) The multiplicative congruential method with 5 0 2, 5, 2 . x a m

(iv) The multiplicative congruential method with 5 0 1, 5, 2 1. x a m = = = −

(v) The multiplicative congruential method with 5 0 1, 3, 2 1. x a m −

(vi) The linear congruential method with 17 0 37911, 9806, 1, 2 1. x a c m = = = = −

(vii) The pseudorandom number generator technique with 0 0, 13, 0.2019. A B u

(viii) The RAND() function in MS Excel. For ( i ) – ( vi ), a number i u is generated using the formula , 1, 2, 3,... i i x ui m ==

(a) For each of the eight random number generators, generate 1000 , i u where 1, 2,...,1000. i = Use these 1000 random numbers to simulate an insurance coverage’s claim size, X , that follows a continuous uniform distribution from 2020 to 3014. ( 10 marks)

(b) Calculate the average claim size simulated by each of the eight random number generators. ( 2 marks)

(c) Compute ( ). EX (2 marks)

(d) Compare and comment on the answers obtained in (b) and (c). Your discussion should include the various desired properties of good random number generator