Question 1

The variance of a discrete distribution increases if we add a positive constant to each one of its value.

Accepted Answer

Adding a positive constant to each value of a discrete distribution will not change the variability of the distribution, as the units of measurement will also change. The variance is a measure of variability that is based on the original units of measurement, not the added constant. Therefore, the variance will remain the same.

Question 2

A variable that can take on values at any point over a given interval is called a discrete random variable.

Accepted Answer

A discrete random variable can only take on specific values within a range, not any value over the interval.

Question 3

Variables which take on values only at certain points over a given interval are called continuous random variables.

Accepted Answer

Variables which take on values only at certain points over a given interval are called discrete random variables, while continuous random variables can take on any value over a given interval.

Question 4

The mean or the expected value of a discrete distribution is the long-run average of the occurrences.

Accepted Answer

The mean or expected value of a discrete distribution is calculated by multiplying each possible outcome by its probability and then adding up all the products. It represents the long-run average of the occurrences of that distribution.

Question 5

The expected monetary payoff of perfect information is the value of perfect information.

Accepted Answer

The answer of The expected monetary payoff of perfect information...

Question 6

To compute the variance of a discrete distribution, it is $\textbf{      not    }$ necessary to know the mean of the distribution.

Accepted Answer

To compute the variance of a discrete distribution, the mean of the distribution is necessary because variance is calculated as the average of the squared differences from the Mean.

Question 7

In a decision analysis problem, variables (such as general macroeconomic conditions) which are $\textbf{     not     }$ under the decision maker's control are called prior probabilities.

Accepted Answer

In decision analysis, variables not under the decision maker's control, such as general macroeconomic conditions, are referred to as external factors or uncertainties, not prior probabilities. Prior probabilities refer to the initial assessments of the likelihood of various states of nature before any additional information is considered.

Question 8

In a decision-making scenario, if it is $\textbf{    not     }$  known which of the states of nature will occur and further if the probabilities of occurrence of the states are also unknown the scenario is called decision-making under double risk.

Accepted Answer

The scenario is called decision-making under uncertainty, not double risk. In decision-making under uncertainty, outcomes of decisions are not known and probabilities of their occurrences are also unknown.

Question 9

In a decision-making under risk scenario, the expected monetary value of a decision alternative is the weighted average (using the probability of each state of nature as the weight) of the payoffs to the decision alternative in each state of the nature.

Accepted Answer

This is the definition of expected monetary value in decision-making under risk.

Question 10

In decision-making under risk, the expected monetary payoff of perfect information is the weighted average of the best payoff for each state of nature (using the probability of the state of nature as the weight).

Accepted Answer

This statement correctly describes the concept of expected monetary value of perfect information.

Question 11

The amount of time a patient waits in a doctor's office is an example of a continuous random variable.

Accepted Answer

This is correct as the waiting time can take on any value within a certain range, rather than being restricted to specific values like a discrete random variable.

Question 12

In a decision-making under uncertainty scenario, the decision maker chooses the decision alternative that has the minimum expected (i.e., probability-weighted) payoff among all the available alternatives.

Accepted Answer

In a decision-making under uncertainty scenario, the decision maker chooses the decision alternative that has the maximum expected (i.e., probability-weighted) payoff among all the available alternatives.

Question 13

The number of visitors to a website each day is an example of a discrete random variable.

Accepted Answer

The number of visitors is a countable and finite value, hence it is an example of a discrete random variable.

Question 14

In a decision analysis problem, variables (such as investing in common stocks or corporate bonds) which are under the decision maker's control are called decision alternatives.

Accepted Answer

This statement is true. The decision alternatives are the options available to the decision maker that they have control over.

Question 15

In a decision analysis problem, variables (such as benefits or rewards that result from investments in common stocks or corporate bonds and from a new product launch) which result from selecting a particular decision alternative are called posterior probabilities.

Accepted Answer

Variables that result from selecting a particular decision alternative are not called posterior probabilities, but rather outcomes or consequences. Posterior probabilities refer to the probabilities of events occurring after considering new information or data.

Question 16

In a decision-making scenario, if it is $\textbf{     not    }$  known which of the states of nature will occur but the probabilities of occurrence of the states are known the scenario is called decision-making under risk.

Accepted Answer

When probabilities of occurrence of the states are known, but not the exact state that will occur, it is a scenario of decision-making under risk.

Question 17

In a decision-making under risk scenario, the expected monetary value of a decision alternative is the arithmetic average of the payoffs to the decision alternative in each state of the nature.

Accepted Answer

The answer of In a decision-making under risk scenario, the...

Question 18

In a decision-making scenario, if the decision maker knows which state of nature will occur, the scenario is called decision-making under certainty.

Accepted Answer

Decision-making under certainty occurs when the decision maker knows with certainty which state of nature will occur.

Question 19

In decision-making under risk, the expected monetary value without information is the largest of the expected monetary values for the various decision alternatives.

Accepted Answer

The expected monetary value without information is calculated by multiplying the probability of each possible outcome by its monetary value and adding up the results. The decision alternative with the highest expected monetary value is the one that should be chosen.

Question 20

The value of perfect information is the difference between the monetary payoff with perfect information and the expected monetary payoff with no information.

Accepted Answer

The statement accurately describes the concept of value of perfect information.

Quiz 6: Decision Analysis and Expected Value

The variance of a discrete distribution increases if we add a positive constant to each one of its value.

A variable that can take on values at any point over a given interval is called a discrete random variable.

Variables which take on values only at certain points over a given interval are called continuous random variables.

The mean or the expected value of a discrete distribution is the long-run average of the occurrences.

The expected monetary payoff of perfect information is the value of perfect information.

To compute the variance of a discrete distribution, it is not \textbf{ not } not necessary to know the mean of the distribution.

In a decision analysis problem, variables (such as general macroeconomic conditions) which are not \textbf{ not } not under the decision maker's control are called prior probabilities.

In a decision-making scenario, if it is not \textbf{ not } not known which of the states of nature will occur and further if the probabilities of occurrence of the states are also unknown the scenario is called decision-making under double risk.

In a decision-making under risk scenario, the expected monetary value of a decision alternative is the weighted average (using the probability of each state of nature as the weight) of the payoffs to the decision alternative in each state of the nature.

In decision-making under risk, the expected monetary payoff of perfect information is the weighted average of the best payoff for each state of nature (using the probability of the state of nature as the weight).

The amount of time a patient waits in a doctor's office is an example of a continuous random variable.

In a decision-making under uncertainty scenario, the decision maker chooses the decision alternative that has the minimum expected (i.e., probability-weighted) payoff among all the available alternatives.

The number of visitors to a website each day is an example of a discrete random variable.

In a decision analysis problem, variables (such as investing in common stocks or corporate bonds) which are under the decision maker's control are called decision alternatives.

In a decision analysis problem, variables (such as benefits or rewards that result from investments in common stocks or corporate bonds and from a new product launch) which result from selecting a particular decision alternative are called posterior probabilities.

In a decision-making scenario, if it is not \textbf{ not } not known which of the states of nature will occur but the probabilities of occurrence of the states are known the scenario is called decision-making under risk.

In a decision-making under risk scenario, the expected monetary value of a decision alternative is the arithmetic average of the payoffs to the decision alternative in each state of the nature.

In a decision-making scenario, if the decision maker knows which state of nature will occur, the scenario is called decision-making under certainty.

In decision-making under risk, the expected monetary value without information is the largest of the expected monetary values for the various decision alternatives.

The value of perfect information is the difference between the monetary payoff with perfect information and the expected monetary payoff with no information.

To compute the variance of a discrete distribution, it is $\textbf{ not }$ necessary to know the mean of the distribution.

In a decision analysis problem, variables (such as general macroeconomic conditions) which are $\textbf{ not }$ under the decision maker's control are called prior probabilities.

In a decision-making scenario, if it is $\textbf{ not }$ known which of the states of nature will occur and further if the probabilities of occurrence of the states are also unknown the scenario is called decision-making under double risk.

In a decision-making scenario, if it is $\textbf{ not }$ known which of the states of nature will occur but the probabilities of occurrence of the states are known the scenario is called decision-making under risk.