McHuffter Condominiums, Inc., of Pensacola, Florida, recently purchased land near the Gulf of Mexico and is attempting to determine the size of the condominium development it should build. Three sizes of development are being considered; Small, d1; Medium, d2; and Large, d3. At the same time, an uncertain economy makes it is difficult to ascertain the demand for new condominiums. McHuffter’s management realizes that a large development followed by a low demand could be very costly to the company. However, if McHuffter makes a conservative small-development decision and then finds a high demand, the firm’s profits will be lower than they might have been. With the three levels of demand-low, medium, and high. McHuffter’s management has prepared the following profit ($000). Payoff Table Decision Alternatives Demand Low Medium High Small, d1 400 500 600 Medium, d2 100 600 800 Large, d3 -300 400 1200 1). If nothing is known about the demand probabilities, what are the recommended decision using the Maximax (optimistic), Maximin (pessimistic) and Equally Likely? 2). If P(low) = 0.20, P(medium) = 0.35, and P(high) = 0.45. What is the recommended decision using the expected monetary value approach? 3). What is the expected value of perfect information (EVPI)?
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
McHuffter Condominiums, Inc., of Pensacola, Florida, recently purchased land near the Gulf of Mexico and is attempting to determine the size of the condominium development it should build. Three sizes of development are being considered; Small, d1; Medium, d2; and Large, d3. At the same time, an uncertain economy makes it is difficult to ascertain the demand for new condominiums. McHuffter’s management realizes that a large development followed by a low demand could be very costly to the company. However, if McHuffter makes a conservative small-development decision and then finds a high demand, the firm’s profits will be lower than they might have been. With the three levels of demand-low, medium, and high. McHuffter’s management has prepared the following profit ($000).
Payoff Table
|
Decision Alternatives |
Demand |
||
|
Low |
Medium |
High |
|
|
Small, d1 |
400 |
500 |
600 |
|
Medium, d2 |
100 |
600 |
800 |
|
Large, d3 |
-300 |
400 |
1200 |
1). If nothing is known about the demand probabilities, what are the recommended decision using the Maximax
(optimistic), Maximin (pessimistic) and Equally Likely?
2). If P(low) = 0.20, P(medium) = 0.35, and P(high) = 0.45. What is the recommended decision using the expected monetary value approach?
3). What is the
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