1 answer

As we've previously seen, equations describing situations often contain uncertain parameters, that is, parameters that aren't...

Question:

As weve previously seen, equations describing situations often contain uncertain parameters, that is, parameters that arent
As we've previously seen, equations describing situations often contain uncertain parameters, that is, parameters that aren't necessarily a single value but instead are associated with a probability distribution function. When more than one of the variables is unknown, the outcome is difficult to visualize. A common way to overcome this difficulty is to simulate the scenario many times and count the number of times different ranges of outcomes occur. One such popular simulation is called a Monte Carlo Simulation. In this problem-solving exercise you will develop a program that will perform a Monte Carlo simulation on a simple profit function. Consider the following total profit function: P1 =nP Where Pr is the total profit, nt is the number of vehicles sold and P, is the profit per vehicle. PARTA Compute 5 iterations of a Monte Carlo simulation given the following information: n follows a uniform distribution with minimum of 1 and maximum 10 P follows a normal distribution with a mean of S7000 and a standard deviation of $1750 Number of bins: 10 Recall that for all practical purposes we will use 3 std. deviations from the mean as the maximum value for parameters following a normal distribution. Obviously, 5 iterations are not very many. In fact, typically you would simulate 10,000 iterations or so to view meaningful results but I figured that I'd give you a break . If you'd like to compute 10,000 iterations by hand for extra credit, go ahead... ii.) What are the ranges for the 10 bins? Fill in the table below: Iteration 3 Iteration + Iteration 5 Parameter Iteration 1 Iteration 2 38 S3750 $4500 S7000 S6700 S7750 S Range

Answers

i)

If normal distribution is chosen with mean $7000 and standard deviation(sd) $1750 then the range is 7000-(3*1750) to 7000 + (3*1750) , which is (1750,12250)

Thus the range is 12250-1750 = 10500. since total number of bins is 10, the size of each bin is 10500/10=1050

Thus the ranges for the bins are

1750-2800, 2800-3850, 3850-4900, 4900-5950, 5950-7000, 7000-8050, 8050-9100, 9100-10150, 10150-11200, 11200-12250

ii)

Pt is obtained by multiplying Pv and n.

Based on the value of Pv it is classified into the bin # based on above bin mapping.

Range of Pv is the same for all iterations based on the above assumed distribution.

The table will be as follows

n 3 8 5 9 6
Pv 3750 4500 7000 6700 7750
Pt 11250 36000 35000 60300 46500
Bin # 2 3 5 5 6
$ Range 10500 10500 10500 10500 10500
.

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