The manager of a construction company must decide whether to build single family homes, apartments, or condominiums. Profits (in thousands of dollars) are given in the following table and depend on various possible population trends. The probability of a declining population is 0.3, the probability for a stable population is 0.5 and the probability of a growing population is 0.2 declining population stable population growing population single family homes 220 80 75 apartments 85 175 100 condominiums -30 90 240 If the manager is an extreme optimist, which alternative would she choose? If the manager is an extreme pessimist, which alternative would she choose? If the manager wants to minimize maximum regret, which alternative should she choose? If the manager wants to maximize expected values, which alternative should she choose? What is the most amount of money that she should be willing to spend to get more information about the possible population trends?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
The manager of a construction company must decide whether to build single family homes, apartments, or condominiums. Profits (in thousands of dollars) are given in the following table and depend on various possible population trends. The probability of a declining population is 0.3, the probability for a stable population is 0.5 and the probability of a growing population is 0.2
| declining population | stable population | growing population | |
| single family homes | 220 | 80 | 75 |
| apartments | 85 | 175 | 100 |
| condominiums | -30 | 90 | 240 |
- If the manager is an extreme optimist, which alternative would she choose?
- If the manager is an extreme pessimist, which alternative would she choose?
- If the manager wants to minimize maximum regret, which alternative should she choose?
- If the manager wants to maximize expected values, which alternative should she choose?
- What is the most amount of money that she should be willing to spend to get more information about the possible population trends?
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