1. Module 9.2 Simulations

2. Computer simulation Having computer program imitate reality, in order to study situations and make decisions Applications?

3. Use simulations if Not feasible to do actual experiments System does not exist Cost of actual experiments prohibitive Money Time Danger Want to test alternatives

4. Monte Carlo simulation Probabilistic model involving element of chance Not deterministic but is probabilistic or stochastic Uses random number generator Each time a simulation is run, results can vary from those of other runs Disadvantages-simulation maybe expensive in time,money to develop -since it is impossible to test every alternatives, only provide goog solution not a best solution –because a sim. Is probabilistic involving an element of chance, should be careful of our conclusions-results maybe difficult to verify cause often don’t have real world data – can’t be sure we understand what simulation actually does

5. Multiplicative Linear Congruential Method-D.J.Lenmer 1949 random 0 = 10 (seed) random n = (7 * random n - 1 ) mod 11(modulus), for n > 0 (generating function) Generates? 10, 4, 6, 9, 8, 1, 7, 5, 2, 3

6. Multiplicative Linear Congruential Method random 0 = seed random n = (multiplier * random n – 1 +increment) mod modulus, for n > 0 Good randon number generator should give as long a sequence as possible, sequence appers random modulus often largest integer comp. can store, such as 2 31 - 1 = 2,147,483,647 One multiplier: 16,807, increment 0

7. Random floating point number For random number, rand, with 0.0 ≤ r and < 1.0 rand = random n /modulus Example r 0 = 10, r n = (7 * r n - 1 ) mod 11, for n > 0 Integers: 10, 4, 6, 9, 8, 1, 7, 5, 2, 3 Floating point: 10/11, 4/11, …, 3/11

8. Different ranges of random numbers How to obtain uniformly distributed integer or real random numbers in any range For 0 ≤ rand < 1, r = (max - min) rand + min Random floating point number min ≤ r < max Example: random floating point number between 20.0 and 26.3? 6.3rand + 20.0

9. Random integer min ≤ n ≤ max For 0 ≤ rand < 1 n = int( (max - min + 1) rand + min) Example: random integer between 20 and 26, inclusively? int(7rand + 20)