Deck 6: Decision Analysis and Expected Value

Question 1

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

Answer 1

False

Question 2

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

Answer 2

False

Question 3

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

Answer 3

False

Question 4

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

Question 5

The expected monetary payoff of perfect information is the value 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.

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.

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.

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.

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).

Question 11

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

Question 13

The number of visitors to a website each day 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.

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.

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.

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.

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.

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.

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.

Question 21

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 ___.

A) payoffs
B) decision alternatives
C) states of nature
D) revised probabilities
E) prior probabilities

Question 22

A market research team compiled the following discrete probability distribution. In this distribution, x represents the number of automobiles owned by a family: Which of the following statements is true?

A) This distribution is skewed to the right.
B) This is a binomial distribution.
C) This is a normal distribution.
D) This distribution is skewed to the left.
E) This distribution is bimodal.

Question 23

The speed at which a jet plane can fly is an example of ___.

A) neither discrete nor continuous random variable
B) both discrete and continuous random variable
C) a continuous random variable
D) a discrete random variable
E) a constant

Question 24

Dianna Ivy is evaluating a plan to expand the production facilities of International Compressors Company which manufactures natural gas compressors. Dianna feels that the price of coal is a significant factor in her decision, but she cannot control it. For her decision, the different prices of coal represent the ___.

A) payoffs
B) decision alternatives
C) states of nature
D) revised probabilities
E) prior probabilities

Question 25

Dan Hein owns the mineral and drilling rights to a 1,000 acre tract of land. If he drills a well and does $\textbf{ not }$ strike oil his net loss will be $50,000, but if he drills a well and strikes oil his net gain will be $100,000. If he does $\textbf{ not }$ drill, his loss is the cost of the mineral and drilling rights, which amount to $1000. For Dan's decision problem, the variable "oil in the tract" is one of the

A) payoffs.
B) decision alternatives.
C) states of nature.
D) revised probabilities.
E) prior probabilities.

Question 26

In American Roulette, there are two zeroes and 36 non-zero numbers (18 red and 18 black). If a player bets 1 unit on red, his chance of winning 1 unit is therefore 18/38 and his chance of losing 1 unit (or winning -1) is 20/38. Let x be the player profit per game. The mean (average) value of x is approximately ___.

A) 0.0526
B) -0.0526
C) 1
D) -1
E) 0

Question 27

A market research team compiled the following discrete probability distribution on the number of soft drinks the average adult drinks each day. In this distribution, x represents the number of sodas which an adult drinks: The standard deviation of x is ___.

A) 1.04
B) 0.89
C) 1.40
D) 1.02
E) .588

Question 28

Dan Hein owns the mineral and drilling rights to a 1,000 acre tract of land. If he drills a well and does $\textbf{ not }$ strike oil his net loss will be $50,000, but if he drills a well and strikes oil his net gain will be $100,000. If he does $\textbf{ not}$ drill, his loss is the cost of the mineral and drilling rights, which amount to $1000. For Dan's decision problem, the variable "drill the well" is one of the ___.

A) payoffs
B) decision alternatives
C) states of nature
D) revised probabilities
E) prior probabilities

Question 29

You are offered an investment opportunity. Its outcomes and probabilities are presented in the following table: Which of the following statements is true?

A) This distribution is skewed to the right.
B) This is a binomial distribution.
C) This distribution is symmetric.
D) This distribution is skewed to the left.
E) This is a Poisson distribution.

Question 30

The volume of liquid in an unopened 5.68 litre can of paint is an example of ___.

A) the binomial distribution
B) both discrete and continuous variable
C) a continuous random variable
D) a discrete random variable
E) a constant

Question 31

A market research team compiled the following discrete probability distribution for families residing in Pictou County. In this distribution, x represents the number of evenings the family dines outside their home during a week: The standard deviation of x is ___.

A) 1.00
B) 2.00
C) 0.80
D) 0.89
E) 1.09

Question 32

A recent analysis of the number of rainy days per month found the following outcomes and probabilities: The standard deviation of this distribution is ___.

A) .800
B) .894
C) .400
D) 4.00
E) .457

Question 33

A market research team compiled the following discrete probability distribution on the number of soft drinks the average adult drinks each day. In this distribution, x represents the number of sodas which an adult drinks: The mean (average) value of x is ___.

A) 1.4
B) 1.75
C) 2.10
D) 2.55
E) 3.02

Question 34

Dan Hein owns the mineral and drilling rights to a 1,000 acre tract of land. If he drills a well and does $\textbf{ not }$ strike oil his net loss will be $50,000, but if he drills a well and strikes oil his net gain will be $100,000. If he does $\textbf{ not }$ drill, his loss is the cost of the mineral and drilling rights, which amount to $1000. For Dan's decision problem, the variable "net loss of $50,000" is one of the

A) payoffs.
B) decision alternatives.
C) states of nature.
D) revised probabilities.
E) prior probabilities.

Question 35

The A-Life Corporation has 320 employees. The Human Resource manager of the corporation documents the frequency with which employees call in sick. In the month of December, 16 employees called in sick 3 times, 48 employees called in sick 2 times, 64 employees called in sick once, and 160 did not call in sick at all.
a) What type of variable is x = 'the number of times employees called in sick'?
b) Develop a probability distribution for the x.

Question 36

The number of finance majors within the School of Business is an example of ___.

A) a discrete random variable
B) a continuous random variable
C) the Poisson distribution
D) the normal distribution
E) a constant

Question 37

A recent analysis of the number of rainy days per month found the following outcomes and probabilities: The mean of this distribution is ___.

A) 2
B) 3
C) 4
D) 5
E) <1

Question 38

The expected monetary value without information is $60, and the expected monetary payoff with perfect information is $120. The expected value of perfect information is

A) $60.
B) $2.
C) $180.
D) $0.50.
E) $120.

Question 39

A market research team compiled the following discrete probability distribution for families residing in Pictou County. In this distribution, x represents the number of evenings the family dines outside their home during a week: The mean (average) value of x is ___.

A) 1.0
B) 1.5
C) 2.0
D) 2.5
E) 3.0

Question 40

The expected monetary value without information is $2,500, and the expected monetary payoff with perfect information is $5,000. The expected value of perfect information is

A) $7,500.
B) $2,500.
C) $1,500.
D) $2,000.
E) $1,250.

Question 41

A market research team compiled the following discrete probability distribution for families residing in Randolph County. In this distribution, x represents the number of evenings the family dines outside their home during a week:
Determine the mean (average) value and standard deviation of x.

Question 42

A dream car lottery is valued at $100,000. The probability of winning the car is 0.001. What is the expected value of the lottery if it costs $50 to play?