In probability terms, a random variable is a numerical
Risk analysis helps the decision maker recognize the
description of the outcome of a random experiment A random difference between the expected value of a decision
variable can be classifies as being either: Discrete or
alternative and the payoff that may actually occur
Continuous
Decision alternative and a state of nature combine to generate
The probability distribution for a random variable describes the payoff associated with a decision
the range and relative likelihood of possible values for a
Risk profile for a decision alternative shows the possible
random variable
payoffs along with their associated probabilities
A probability that is generated from observations is called an Sensitivity analysis determines how changes in the
empirical probability distribution
probabilities for the states of nature or changes in the payoffs
An empirical probability is considered a custom discrete
affect the recommended decision alternative
probability distribution if it is discrete and the possible values Decision makers have the ability to collect additional
of the random variable have different values
information about the states of nature
Variance is a measure of variability
Additional information is obtained through experiments
The standard deviation, σ, is defined as the positive square designed to provide sample information about the states of
root of the variance
nature The preliminary or prior probability assessments for
A binomial probability distribution: discrete probability
the states of nature that are the best probability values
distribution used to describe many situations which fixed
available prior to obtaining additional information Posterior
number (n) of repeated identical and independent trials has probabilities are revised probabilities after obtaining
two, and only two, possible outcomes:Success,Failure
additional information
Poisson Probability Distribtion A discrete random variable
A special case of gaining additional information related to a
that is often useful in estimating the number of occurrences of decision problem is when the sample information provides
an event over a specified interval of time and space Ex:
perfect information on the states of nature
Number of patients who arrive at a health care clinic in one Discrete random variables – the probability mass function f(x)
hour, Number of computer-server failures in a month
provides the probability that the random variable assumes a
Discrete random variables: the probability mass function f(x) particular value
provides the probability that the random variable assumes a Uniform- With every interval of a given length being equally
particular value
likely, the random variable x is said to have a uniform
Continuous random variables: the counterpart of the
probability of distribution
probability mass function is the probability density function, The uncertain future events, referred to as chance events
also denoted by f(x)
The outcomes associated with each combination of decision
One of the most useful probability distributions for describing alternative and chance event outcome
a continuous random variable is the normal probability
Quiz 6
distribution Ex: heights and weights of people, test scores,
An experiment consists of determining the speed of
scientific measures
automobiles on a highway by the use of radar equipment. The
The exponential probability distribution ex:Time between
random variable in this experiment is which of the following?a
patient arrivals at an emergency room,
continuous random variable
Distance between major defects in a highway
Which of the following gives the proportion of items in each
Probability distribution: Represents not only the range of
bin?relative frequency
possible values but also the relative likelihood of various
Which of the following best describes the definition of a
outcomes
probability?numerical measure of the likelihood that an
A simulation model extends the spreadsheet modeling
event will occur
approach by replacing the use of single values for parameters
The random variable X is known to be uniformly distributed
with a probability distribution of possible values
between 5 and 15. Compute E(X), the expected value of the
Parameters that are not known with a high degree of certainty
distribution. 10
are called random, or uncertain, variables
The random variable X is known to be uniformly distributed
The values for random variables are randomly generated from
between 5 and 13. Compute the standard deviation of X.
the specified probability distributions
2.309
Simulation results help us to make decision recommendations
All of the following are examples of discrete random variables
for the controllable inputs that address not only the average
except which of the following? Time
output but also the variability of the output
In a normal distribution, which is greater, the mean or the
Decision makers are interested in risk analysis, that is,
median?neither the mean nor the median (they are equal)
quantifying the likelihood and magnitude of an undesirable
A variable that can only take on specific numeric values is
outcome
called which of the following?Discrete random variable
Verification: process of determining that the computer
Which of the following is not a characteristic of the normal
procedure that performs the simulation calculations is logically
probability distribution?The standard deviation must be 1.
correct
Which statement is true about mutually exclusive events?
Validation: process of ensuring that the simulation model
If events A and B cannot occur at the same time, they are
provides an accurate representation of a real system
called mutually exclusive.
Risk analysis helps to provide the probability information
A survey of 100 random high school students finds that 84
about the favorable as well as the unfavorable outcomes that
students watched the Super Bowl, 27 students watched the
may occur
Stanley Cup Finals, and 18 studentswatched both games. How
Decision analysis considers problems that involve reasonably
many students did not watch either game?7
few decision alternatives and reasonably few possible future
What is the total area under the normal distribution curve?1
events
In a survey of patients in a local hospital, 62.42% of the
In decision analysis, the possible outcomes for a chance event
respondents indicated that the health care providers needed
are the states of nature
to spend more time with each patient. Who makes up the
Payoff the outcome resulting from a specific combination of a
population?All patients in a local hospital
decision alternative and a state of nature
Which of the following involves considering alternative values
Payoff table table showing payoffs for all combinations of
for the random variables and computing the resulting value for
decision alternatives and states of nature
the output?A what-if analysis
A decision tree provides a graphical representation of the
The values for random variables in a Monte Carlo simulation
decision-making process; Shows the natural or logical
are which of the following?generated randomly from
progression that will occur over time
probability distributions
Nodes are used to represent decisions and chance events
Which of the following Excel functions would generate random
Squares are used to depict decision nodes, circles are used to
integers from 0 to 100?=RANDBETWEEN(0, 100)
depict chance nodes
The outcome of a simulation experiment is which of the
The branches connect the nodes; those leaving the decision
following?a probability distribution for one or more output
node correspond to the decision alternatives
measures
Decision analysis without probabilities is appropriate in
In which of the following can a random variable take any value
situations:In which a simple best-case and worst-case analysis
in a specified range?a continuous probability distribution
is sufficient ; Where the decision maker has little confidence in
Which of the following uses repeated random sampling to
his or her ability to assess the probabilities
represent uncertainty in a model representing a real system
The optimistic approach evaluates each decision alternative in
and computes the values of model outputs?Monte Carlo
terms of the best payoff that can occur
simulation
The decision alternative that is recommended is the one that
The choice of the probability distribution for a random variable
provides the best possible payoff
can be guided by which of the following?historical data
For a maximization problem, it is often referred as the
A set of values for the random variables is called which of the
maximax approach
following?A trial
For minimization problems, this approach leads to choosing
All the values of computer-generated random numbers are
the alternative with the smallest payoff
which of the following?uniformly distributed
The corresponding terminology is minimin
Which of the following is an input to a simulation model
The conservative approach evaluates each decision alternative
whose value is uncertain and described by a probability
in terms of the worst payoff that can occur
distribution.a random variable
The decision alternative recommended is the one that
In a base-case scenario, the output is determined by assuming
provides the best of the worst possible payoffs
which of the following?the most likely values for the random
For a maximization problem, it is often referred as the
variables of a model
maximin approach
Which of the following functions computes a value such that
The corresponding terminology is minimax
0.5% of the area under the standard normal distribution lies in
Regret is the difference between the payoff associated with a
the upper tail defined by this value?=NORM.S.INV(0.995)
particular decision alternative and the payoff associated with
The weekly demand for an item in a retail store follows a
the decision that would yield the most desirable payoff for a
uniform distribution over the range 78 to 91. What would be
given state of nature
the weekly demand if its corresponding computer-generated
Regret is often referred to as opportunity loss
value is 0.5?84.5
Under the minimax regret approach, one would choose the
An input to a simulation model that is selected by the decision
decision alternative that minimizes the maximum state of
maker is known as which of the following?
regret that could occur over all possible states of nature
a controllable input
The expected value (EV) of a decision alternative is the sum of
weighted payoffs for the decision alternative
The process of determining that a computer program
implements a simulation model as it is intended is known as
which of the following?verification
What is an intersection or junction point of a decision tree
called?node
Which of the following evaluate each decision alternative in
terms of the best payoff that can occur?the optimistic
approach
When a decision maker is faced with several alternatives and
an uncertain set of future events, s/he uses which of the
following to develop an optimal strategy?decision analysis
Which of the following are possible outcomes for chance
events that affect the consequences associated with a decision
alternative?States of nature
The amount of loss (lower profit or higher cost) from not
making the best decision for each state of nature is known as
which of the following?opportunity loss
An uncertain future event affecting the consequence
associated with a decision is known as which of the
following?A chance event
The weighted average of the payoffs for a chance node is
known as which of the following?Excepted value
The study of how changes in the probability assessments for
the states of nature or changes in the payoffs affect the
recommended decision alternative is known as which of the
following?Sensitivity analysis
Which of the following refers to the result obtained when a
decision alternative is chosen and a chance event occurs?
An outcome
Which of the following are graphical representations of the
decision problems that show the sequential nature of the
decision-making process.Decision trees
Utility theory is the study of the _____ or relative desirability
of a particular outcome that reflects the decision maker's
attitude toward a collection of factors, such as profit, loss, and
risk.Total worth
New information obtained through research or
experimentation that enables an updating or revision of the
state-of-nature probabilities is known as which of the
following?Sample information
The states of nature are defined so that they are which of the
following, meaning that at least one state of nature must occur
at a given time for a chance event?collectively exhaustive
Which of the following is a measure of the total worth of a
consequence reflecting a decision maker's attitude toward
considerations such as profit, loss, and risk?utility
Monte Carlo simulation explanation:
Uncertainty pervades decision-making in business,
government, and our personal lives
Monte Carlo simulation: used to evaluate the impact of
uncertainty on a decision
Simulation models have been successfully used in a variety of
disciplines
Financial applications include investment planning, project
selection, and option pricing
Marketing applications include new product development and
the timing of market entry for a product
Management applications include project management,
inventory ordering, capacity planning, and revenue
management
Probability distribution: Represents not only the range of
possible values but also the relative likelihood of various
outcomes
A simulation model extends the spreadsheet modeling
approach by replacing the use of single values for parameters
with a probability distribution of possible values
Parameters that are not known with a high degree of certainty
are called random, or uncertain, variables
The values for random variables are randomly generated from
the specified probability distributions
Simulation results help us to make decision recommendations
for the controllable inputs that address not only the average
output but also the variability of the output
Advantages and Disadvantages of Monte Carlo
For complex systems, the process of developing, verifying, and
validating a simulation model can be time-consuming and
expensive
As with all mathematical models, the analyst must be
conscious of the assumptions of the model in order to
understand its limitations
The summary of the simulation data provides only estimates
or approximations about the real system