You have simulated two systems and made 10 simulation runs of each, estimating p

Question

You have simulated two systems and made 10 simulation runs of each, estimating profit (which you want to maximize) for each system. The same random number seeds were used for each system. Assume sample sizes of 1. Calculate the probability that each system is best with respect to profit (show calculations). For System A profit above, identify the 80% confidence interval of the mean based on samples of size 1 (z value 1.28) For System A profit above, identify the 80% certainty interval of the data In the data above, the correlation in profits between Systems A and B is 0.999. Are the results for Systems A & B independent? What does that imply about the probability estimates of relative profitability in questions 2 & 3?

Explanation / Answer

Answer to question# 1)

The system with least Z error would be the best

Mean standard error = Mean / Standard deivation

.
for system A we get:

Mean standard error = 137412 / 243802 = 0.5636

.

for system B we get:

Mean standard error = 301083 / 463224 = 0.6450

.

For System C:

Mean standard error = 342306 / 536365 = 0.6382

.

Thus of all the three systems . system A has the least error

and thus it is considered to be the best

.

Answer to questioN# 2)

Formula of confidence interval is :

Mean - z* s/ n , Mean + z*s/n

For System A we got :

Mean = 137412

s = standard deviaton = 243802

n = 1 ......[stated in the question consider sample size to be 1]

z = 1.28....[as given in the question]

.

On pluggging these vlaues we get:

137412 - 1.28 * 243802 / 1 , 137412 + 1.28 * 243802 / 1

137412 - 312066.56 , 137412 + 312066.56

-174654.56 , 449478.56

.

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