Question a) Why do we have to build models instead of carrying out the experiment on the actual systems? AN (5 marks) b) Simulation models are not the only models that can be used for understanding and improving the real world. There exist other modeling approaches. Why would simulation be used in preference to these other modeling approaches. CR (5 marks) c) Consider an unfair six-sided die where the probability of rolling a 1 is three times the probability of rolling any other value. All other values have the same probability of occurring. Let X be the random variable that takes on values 1 through 6 for our unfair die. Plot the pmf and CDF of X. Determine the mean of X. EV (10 marks)