You need to hire some new employees to staff your startup venture. You know that potential employees are distributed throughout the population as follows, but you can't distinguish among them: Employee Value Probability $45,000 0.25 $64,000 0.25 $83,000 0.25 $102,000 0.25 The expected value of hiring one employee is . Suppose you set the salary of the position equal to the expected value of an employee. Assume that employees will not work for a salary below their employee value. The expected value of an employee who would apply for the position, at this salary, is . Given this adverse selection, your most reasonable salary offer (that ensures you do not lose money) is
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!
7 . Individual Problems 19-6
|
Employee Value
|
Probability
|
|---|---|
| $45,000 | 0.25 |
| $64,000 | 0.25 |
| $83,000 | 0.25 |
| $102,000 | 0.25 |
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