Exam 15: Introduction to Simulation Modeling

(A)Use @RISK distributions to generate the three random variables and derive a distribution for the amount of reserves.What is the amount we can expect to recover from this field? (B)The production output is a product of three very different types of input distributions.What does the output distribution look like? What are the implications of the shape of this distribution? (C)What is the standard deviation of the recoverable reserves? What are the 5th and 95th percentiles of this distribution? What does this imply about the uncertainty in estimating the amount of recoverable reserves? (D)Suppose you think oil price is normally distributed with a mean of $65 per barrel and a standard deviation of $10.How much revenue do you expect the field produce (ignore discounting)? (E)Finally,your engineer is uncertain about costs to drill wells to develop the field,but she thinks the most likely cost will be $1.7Bn,although it could be as much as $3Bn or as little as $1Bn.What is your expected profit from the field? (F)What is the chance that you will loose money? Is this a risky venture?

Some important characteristics of probability distributions in general include the following distinctions:

Which of the following statements is true regarding the Triangular distribution?

Correlation between two random input variables might not change the mean of an output,but it can definitely affect the variability and shape of an output disbribution.

(A)Generate the "birthdays" of 30 different people,assuming that each person has a 1/365 chance of having a given birthday (call the days of the year 1,2,3,……..,365).You can use a formula involving the INT and RAND functions to generate birthdays. (B)Once you have generated 30 people's birthdays,you can tell whether at least two people have the same birthday using Excel's RANK function (i.e.,in the case of a tie,two numbers are given the same rank).Do you see any people with the same birthday in your sample? (C)Obtain at least 20 samples of the 30 person group using the F9 key.What do you estimate the probability of finding two people with the same birthday in a sample of 30 people to be?

(A)Company experts have no idea what the distribution of the development cost is.All they can state is that "we are 90% sure it will be somewhere between $450,000 and $650,000." (B)Company experts can still make the same two statements as in (A),but now they can also state that "we believe the distribution is symmetric and its most likely value is about $550,000." (C)Company experts can still make the same two statements as in (A),but now they can also state that "we believe the distribution is skewed to the right,and its most likely value is about $500,000."

Which of the following statements is true regarding the Normal distribution?

If you add several normally distributed random numbers,the result is normally distributed,where the mean of the sum is the sum of the individual means,and the variance of the sum is the sum of the individual variances.This result is difficult to prove mathematically,but it is easy to demonstrate with simulation.To do so,run a simulation where you add three normally distributed random numbers,each with mean 100 and standard deviation 10.Your single output variable should be the sum of these three numbers.Verify with @RISK that the distribution of this output is approximately normal with mean 300 and variance 300 (hence,standard deviation = 17.32).

@Risk introduces uncertainty explicitly into a spreadsheet model by allowing several inputs to have probability distributions and then enabling the simulation of random values from these inputs.

The Excel RAND()function generates random numbers from a Normal(0,1)distribution.

A common guideline in constructing confidence intervals for the mean is to place upper and lower bounds one standard error on either side of the average to obtain an approximate 95% confidence interval.

The flaw of averages is the reason deterministic models can be very misleading.

If we want to model the monthly return on a stock,we might choose

RISKSIMTABLE is a function in @Risk for running several simulations simultaneously,one for each setting of an input or decision variable.

The RAND()function in excel models which of the following probability distributions:

The deterministic (non-simulation)approach,using best guesses for the uncertain inputs,is:

A correlation matrix must always be symmetric,so that the correlations above the diagonal are a mirror image of those below it.

(A)What are the appropriate probability distributions to model the number of faculty members showing up in each lot? (B)Given the current situation,estimate the probability that on a peak day,at least one faculty member with a sticker will be unable to find a parking space.Assume that the number who shows up at each lot is independent of the number who shows up at the other two lots. (C)Suppose that faculty members are allowed to park in any lot.Does this help solve the problem? Why or why not? (D)Suppose that the numbers of faculty who show up at the three lots are correlated,with each correlation equal to 0.80.Does your answer to (C)change? Why or why not?

Many companies have used simulation to determine which of several possible investment projects they should choose.This is often referred to as

Analysts often plan a simulation so that the confidence interval for the mean of some important output will be sufficiently narrow.The reasoning is that narrow confidence intervals imply more precision about the estimated mean of the output variable.