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Question: Most of us have a hard time assessing probabilities with much precision. For instance, in assessing the probability of rain tomorrow, even carefully considering the lotteries and trying to adjust a wheel of fortune to find the indifference point, many people would eventually say something like this: "If you set p = 0.2, I'd take Lottery A, and if p = 0.3, I'd take Lottery B. My indifference point must be somewhere in between these two numbers, but I am not sure where." How could you deal with this kind of imprecision in a decision analysis? Illustrate how your approach would work using the umbrella problem (Figure).
(The question is not how to get more precise assessments. Rather, given that the decision maker refuses to make precise assessments, and you are stuck with imprecise assessments, what kinds of decision-analysis techniques could you apply to help the individual make a decision?)
Consider the soft drink delivery time data in Example. Find an approximate 95% bootstrap confidence interval on the regression coefficient for distance using.
An electronic module used by the Navy in a sonar device requires replacement on the average once every 16 months and fails according to a Poisson process.
What will be the effect on the following of fixing a minimum wage above the market equilibrium level.
Your uncle has just announced that he's going to give you $10,000 per year at the end of each of the next 4 years (he's less generous than your grandmother).
The director of graduate admissions at a local university is analyzing the relationship between scores on the Graduate Record Examination (GRE).
Use 4th order Runge-Kutta Method with step size h =0.2 and h =0.1 to find y(2) and sketch all the solutions on the interval [1, 2] with appropriate legend for comparison.
Run a regression of the natural logarithm of sales on all the following: price, print marketing expenditure, outdoor marketing expenditure and previous years' sales
Find the Laplace transform and also find the inverse Laplace transform
The Chi-square test for independence is an extension of the goodness of fit test to see if multiple groups are distributed according to expected distributions for each variable.
As indicated above, a band limited communication channel can be modeled as a linear filter whose frequency response characteristics match the frequency.
In a competitive market, the supply schedules is p = 4 + 0.25q and the demand schedule is p = 16 - 0.5q. What would happen to the price paid by consumers.
Find an equation for the speed of the liquid as a function of the distance y it has fallen. Combining this with the equation of continuity, find an expression for the radius of the stream as a function of y.
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