# Question: Simulation can be used to illustrate a number of results

Simulation can be used to illustrate a number of results from statistics that are difficult to understand with non-simulation arguments. One is the famous central limit theorem, which says that if you sample enough values from any population distribution and then average these values, the resulting average will be approximately normally distributed. Confirm this by using @RISK with the following population distributions (run a separate simulation for each):

(a) Discrete with possible values 1 and 2 and probabilities 0.2 and 0.8;

(b) Exponential with mean;

(c) Triangular with minimum, most likely and maximum values equal to 1, 9, and 10. Run each simulation with 10 values in each average, and run 1000 iterations to simulate 1000 averages. Create a histogram of the averages to see whether it is indeed bell-shaped. Then repeat, using 30 values in each average. Are the histograms based on 10 values qualitatively different from those based on 30?

(a) Discrete with possible values 1 and 2 and probabilities 0.2 and 0.8;

(b) Exponential with mean;

(c) Triangular with minimum, most likely and maximum values equal to 1, 9, and 10. Run each simulation with 10 values in each average, and run 1000 iterations to simulate 1000 averages. Create a histogram of the averages to see whether it is indeed bell-shaped. Then repeat, using 30 values in each average. Are the histograms based on 10 values qualitatively different from those based on 30?

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