Deck 15: Introduction to Simulation Modeling

Question 1

One of the primary advantages of simulation models that they enable managers to answer what-if questions about changes in systems without actually changing the systems themselves.

Answer 1

True

Question 2

When we maximize or minimize the value of a decision variable by running several simulations simultaneously,we have found an optimal solution to the problem and attitude toward risk becomes irrelevant.

Answer 2

False

Question 3

Data tables in spreadsheet simulations are useful for taking a "prototype" simulation and replicating its key results a desired number of times.

Answer 3

True

Question 4

A probability distribution is continuous if its possible values are essentially some continuum.

Question 5

If we want to model a random stock price,we should do so with an unbounded symmetric probability distribution.

Question 6

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.

Question 7

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

Question 8

The normal distribution is often used in simulation models because it is the most common distribution in statistics and it does not allow negative values.

Question 9

When we run simulation,the @Risk automatically keeps statistics such as averages and standard deviations,and can also create graphs such as histograms based on the values generated in the output cells in the simulation model.

Question 10

A probability distribution is bounded if there are values A and B such that only one possible value can be less than A or greater than B.

Question 11

Excel's built-in functions,along with the RAND function,can be used to generate random numbers from many different types of probability distributions.

Question 12

The triangular distribution is sometimes used in simulation models because it is more flexible and intuitive than the normal distribution.

Question 13

Sometimes it is convenient to treat a discrete probability distribution as continuous,and vice versa.

Question 14

A discrete distribution is useful for many situations,either when the uncertain quantity is not really continuous (the number of televisions demanded,for example)or when you want a discrete approximation to a continuous variable.

Question 15

A correlation matrix must always have 1's along its diagonal (because a variable is always perfectly correlated with itself)and the correlations between variables elsewhere.

Question 16

The "random" numbers generated by the RAND function (or by any other package's random number generator)are not really random.

Question 17

It is common in computer simulations to estimate the mean of some distribution by the average of the simulated observations.The usual practice is then to accompany this estimate with a confidence interval,which indicates the accuracy of the estimate.

Question 18

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

Question 19

The binomial distribution can be well approximated by the normal distribution when the number of trials n is sufficiently small and the probability of success p is not too close to 0 or 1.

Question 20

Spreadsheet simulation modeling is quite similar to the other modeling applications in that it begins with input variables and then relates these with appropriate Excel formulas to produce output variables of interest.

Question 21

The uniform distribution is bounded by a minimum and a maximum,and all values between these two extremes are equally likely.

Question 22

We typically choose between a symmetric and skewed distribution on the basis of practical modeling issues.

Question 23

The three parameters required to specify a triangular distribution are the minimum,mean and maximum.

Question 24

When n is reasonably large and p isn't too close to 0 or 1,the binomial distribution can be well approximated by which of the following distributions?

A) Uniform distribution
B) Normal distribution
C) Triangular distribution
D) None of these options

Question 25

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.

Question 26

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

Question 27

The binomial distribution is a discrete distribution that is applied to situations where n independent and identical "trials" occur,with each trial resulting in a "success" or "failure," and we want to generate the random number of successes in the n trials.

Question 28

@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.

Question 29

If a model contains uncertain outputs,it can be very misleading to build a deterministic model by using the means of the inputs to predict an output.This is called the:

A) Law of Large Numbers.
B) Flaw of Averages
C) Law of Inevitable Disappointment
D) Central Limit Theorem

Question 30

A primary difference between standard spreadsheet models and simulation models is that at least one of the input variable cells in a simulation model contains random numbers.

Question 31

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

A) Normal(0,1)
B) Uniform(0,1)
C) Normal(-1,1)
D) Uniform(-1,1).

Question 32

When you try to find the most appropriate input probability distribution in a simulation model,you first have to choose the most appropriate family,and then you have to select the most appropriate member of that family

Question 33

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

Question 34

Different random numbers generated by the computer are probabilistically dependent.This implies that when we generate a random number in a particular cell,it has some effect on the values of any other random numbers generated in the spreadsheet.

Question 35

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.

Question 36

A continuous probability distribution is characterized by a:

A) mean and a standard deviation.
B) mean and a variance.
C) density function.
D) histogram

Question 37

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

A) better to use in complicated real world applications.
B) a good estimate of what the answer will be using a simulation approach.
C) generally not the appropriate model.
D) the preferred approach when there is correlation between input variables.

Question 38

We can think of the uniform distribution as:

A) the "I have no idea" distribution.
B) a skewed distribution.
C) only modeling positive values.
D) nonnegative.

Question 39

Which of the following statements are true?

A) The @RISK contains a number of functions such as RISKNORMAL and RISKDISCRETE that make it easy to generate observations from the most important probability distributions.
B) You can specify any cell or range of cells in your simulation model as output cells.
When you run the simulation,@RISK automatically keeps summary measures (averages,standard deviation,percentiles,and others)from the values generated in these output cells across the replications.
C) @RISK has a special function,RISKSIMTABLE,which allows you to run the same simulation several times,using a different value of some key input variable each time.
D) All of these options.

Question 40

It is usually not too difficult to predict the shape of the output distribution from the shape(s)of the input distribution(s).

Question 41

Which of the following statements is correct regarding the graph of a discrete probability distribution?

A) It is a series of spikes.
B) The height of each spike is the probability of the corresponding value.
C) There is an empty space between adjacent spikes.
D) All of these options

Question 42

Which of the following statements are false?

A) A probability distribution is discrete if it has a finite number of possible values.
B) A probability distribution is continuous if its possible values are essentially some continuum.
C) An example of a discrete probability distribution is the amount of rain that falls during the month of June in Michigan.
D) None of these options

Question 43

Suppose you run a simulation model several times with different order quantities.What can we infer about the quantity that maximizes the output,the company's profit?

A) This quantity is the optimal order quantity.
B) This quantity might be the optimal order quantity,but we also need to consider the company's attitude toward risk.
C) This is not necessarily the optimal order quantity,because it may have produced the largest profit by luck.
D) We can't infer anything.

Question 44

One important special use of bounded distributions is when the only possible values are:

A) less than zero.
B) uniformly distributed around the mean.
C) skewed to the right.
D) nonnegative.

Question 45

Each different set of values obtained for the uncertain quantities in a simulation model can considered to be:

A) the mean of the probability distribution.
B) a scenario.
C) a best guess.
D) all of these options.

Question 46

A probability distribution is bounded if there are values A and B such that:

A) A and B represent the 95% confidence interval
B) A and B are the mean and standard deviation,respectively.
C) A and B are the mean and variance,respectively.
D) no value can be less than A or greater than B.

Question 47

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

A) risk analysis
B) @RISK investment
C) unbounded risk
D) None of the above

Question 48

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

A) It is always the appropriate distribution in simulation modeling
B) It does not permit negative values
C) There is a 95% chance that values will be within ± 2 standard deviations of the mean
D) All of these options

Question 49

Which of the following statements are false regarding the numbers generated by the RAND function in Excel?

A) The numbers are random between 0 and 1
B) The numbers are probabilistically dependent
 
C) The numbers are probabilistically independent
D) The numbers are uniformly distributed between 0 and 1

Question 50

It is simple to generate a uniformly distributed random number with a minimum and maximum other than 0 and 1.For example,the formula =150+100 $\text { * }$
RAND()generates a number uniformly distributed between

A) 100 and 150
B) 150 and 250
C) 50 and 100
D) 50 and 250

Question 51

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

A) symmetric distribution around 0
B) positively skewed distribution
C) negatively skewed distribution
D) All of these options

Question 52

Which of the following statements are true?

A) A probability distribution is symmetric (around some point)if the distribution to the left of the point is a mirror image of the distribution to the right of the point.
B) We say a distribution is skewed to the right (or positively skewed)if the "longer tail" is the right tail.
C) We say a distribution is skewed to the left (or negatively skewed)if the "longer tail" is the left tail.
D) All of the above

Question 53

Which of the following statements is (are)false regarding the numbers generated by the RAND function in Excel?

A) Approximately 10% of the numbers will be between 0.0 and 1.0
B) Approximately 20% of the numbers will be between 0.50 and 0.70
C) Approximately 40% of the numbers will be between 0.20 and 0.60
D) Approximately 60% of the numbers will be between 0.15 and 0.75
E) All of these options are false

Question 54

If we want to model the time it takes to serve a customer at a bank,we will probably choose

A) symmetric distribution
B) positively skewed distribution
C) negatively skewed distribution
D) All of these options

Question 55

In order to generate random numbers in Excel from a discrete distribution with a finite number of possible values and corresponding probabilities,we can use

A) only the RAND function
B) only the VLOOKUP function
C) only the VLOOKDOWN function
D) the RAND function along with a VLOOKUP function

Question 56

Which of the following statements are false regarding the graph of a continuous probability distribution?

A) It is characterized by a density function,a smooth curve.
B) It is a series of spikes
C) The height of the density curve above any point is not actually a probability-that is,it is not necessarily between 0 and 1.
D) Heights above the density function indicate relative likelihoods but are not necessarily values between 0 and 1.

Question 57

Simulation models are particularly useful for:

A) forecasting.
B) obtaining deterministic outputs.
C) evaluating constraints.
D) asking what-if questions.

Question 58

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

A) It is a discrete distribution with a minimum,maximum and most likely value
B) It is more flexible and intuitive than the normal distribution
C) It is a symmetric distribution
D) All of these options

Question 59

We sometimes use discrete distributions in place of continuous distributions:

A) because they are more accurate.
B) because they are more simple.
C) when we don't know the mean and variance of the distribution.
D) when we need to generate a histogram

Question 60

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

A) Discrete versus continuous
B) Symmetric versus skewed
C) Bounded versus unbounded
D) Positive (or nonnegative)versus unrestricted
E) All of these options

Question 61

The "building blocks" of all spreadsheet simulation models are:

A) deterministic inputs
B) random numbers between 0 and 1
C) decision variables
D) probability distributions

Question 62

Which of the following statements is true regarding a simulation model?

A) It explicitly models decision-making under uncertainty
B) It explicitly incorporates uncertainty in one or more input variables
C) It provides probability distributions for all outputs,rather than expected values
D) All of these options

Question 63

Assume that x is a random number between 0 and 1,and that the number of units expected to be sold is uniformly distributed between 300 and 500.Then,sales are given by the expression

A) 300 + x
B) 500 - x
C) 300 + 200 x
D) 500 - 200 x
E) 300 + 500 x
Generate a set of 40 random numbers in a column in an Excel spreadsheet by using RAND function.Fix the set of random numbers by copying the column to another column and using the "Paste Special" command with the "Values" option selected.

Question 64

Obtain another set random numbers by pressing the F9 (recalculate)key.Do your results change significantly? Do the changes match your expectations? Explain your answer.
Suppose you are going to invest equal amounts in three stocks.The annual return from each stock is normally with mean 0.01 (1%)and standard deviation 0.06.The annual return on your portfolio,the output variable of interest,is the average of the three stock returns.Run @RISK,using 1000 iterations,on each of the scenarios described in the questions below,and report few results from the summary report sheets.