Cheryl is considering purchasing additional sewing machines to accommodate the increasing demand for her cosplay costumes. Her alternatives are to buy 1 machine, 2 machines, or 3 machines. The profits realized under each alternative are a function of whether her proposal to bid for clothing the official Bandai team is accepted or not. The payoff table below illustrates the profits realized (in $000's) based on the different scenarios Cheryl faces. The probability that her proposal will be accepted is 65%. Alternative Proposal Accepted Proposal Rejected Purchase 1 sewing machine $10 $5 Purchase 2 sewing machines $30 $4 Purchase 3 sewing machines $40 $2 What alternative should Cherly select if she is pessimistic? What alternative should Cherly select based on a criterion of realism with ?α = 0.8?
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!
Cheryl is considering purchasing additional sewing machines to accommodate the increasing demand for her cosplay costumes. Her alternatives are to buy 1 machine, 2 machines, or 3 machines. The profits realized under each alternative are a
|
Alternative |
Proposal Accepted |
Proposal Rejected |
|
Purchase 1 sewing machine |
$10 |
$5 |
|
Purchase 2 sewing machines |
$30 |
$4 |
|
Purchase 3 sewing machines |
$40 |
$2 |
What alternative should Cherly select if she is pessimistic?
What alternative should Cherly select based on a criterion of realism with ?α = 0.8?
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