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(Duality Gap of the Knapsack Problem) Given objects i = 1,...,n with positive weights wi and values vi, we want to assemble a subset of the objects so that the sum of the weights of the subset does not exceed a given T > 0, and the sum of the values of the subset is maximized. This is the knapsack problem, which is a special case of a generalized assignment problem
so that the relative value of the duality gap tends to 0 as k → ∞. Note: This exercise illustrates a generic property of many separable problems with integer constraints: as the number of variables increases, the duality gap decreases in relative terms (see Bertsekas [1982], Section 5.5, or Bertsekas [1995b], Section 5.1, for an analysis and a geometrical interpretation of this phenomenon).
with loss function L(θ,a)= w(θ)(θ-a)^2, where w(θ) is a fixed weighted function. Determine the Bayes rule and comment on the role of w(θ) in this problem.
out of 87 observations 67 were successes. ho p 0.54. confidence level 98. what is the value of the appropriate test
The uniform distribution over the interval 7.5 to 10.5 gallons per minute. Find the probability that between 8.0 gallons and 9.0 gallons are pumped during a randomly selected minute.
Based on probability you calculated in part a, would you conclude that more than 30 percent of Americans (18 years or older) say that figure skating is their favorite Winter Olympic event?
(a) What proportion of customers enter the system? (b) What proportion of entering customers receive service from B? (c) What is the average number of customers in the system? (d) What is the average amount of time that an enterin..
The confidence interval for proportion of adults who approve of the candidate is ____
She then uses the mean and standard deviation of these values to estimate the mean value for all parts the operator is making. Construct a 95% confidence interval for the mean value assuming a normal distribution.
in a study of redgreen color blindness 950 men and 2000 women are randomly selected and tested. among the men 83 have
This question related to Basic Statistics and discuss about calculation of range, interquartile range, variance and standard deviation
From Jackson (2016): Chapter Exercises #1, 2, and 4 only for Ch. 9 (p. 252-253). What is the purpose of conducting an experiment? How does an experimental design accomplish its purpose? In an educational study, what are the advantages and disadvantag..
In order to verify the accuracy of their financial accounts, companies use auditors on a regular basis to verify accounting entries. The company's employees make erroneous entries 5% of the time. Suppose that an auditor randomly checks three entri..
The number of arrivals per minute at a bank located in the central business district of a large city was recorded over a period of 200 minutes, with the following results:
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