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The Quiz Problem) Consider a quiz contest where a person is given a list of N questions and can answer these questions in any order he chooses. Question i will be answered correctly with probability pi, independently of earlier answers, and the person will then receive a reward Ri. At the first incorrect answer, the quiz terminates and the person is allowed to keep his previous rewards. The problem is to maximize the expected reward by choosing optimally the ordering of the questions.
(a) Show that to maximize the expected reward, questions should be answered in decreasing order of piRi/(1 - pi
(b) Consider the variant of the problem where there is a maximum number of questions that can be answered, which is smaller than the number of questions that are available. Show that it is not necessarily optimal to answer the questions in order of decreasing
(c) Give a 2-OPT algorithm to solve the problem where the number of available questions is one more than the maximum number of questions that can be answered.
Summarize the blog entry that you have read. Next, explain the manner in which Nate Silver's analysis in your chosen blog entry addresses the salient points of one particular topic related to this class.
the speed at which you can log into a website through a smartphone is an important quality charactersitc of that
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(a) Carry out a maximum likelihood factor analysis using the correlation matrix of Table 6.17. How many common factors are retained using (i) likelihood ratio chi-squared test, (ii) Akaike's criterion, and (iii) Schwartz's criterion. What ..
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You have been asked to analyse Grand Plomp Ltd, a maker of rocket widgets used by NASA. The owners are wondering whether the return received is sufficient to justify the risks taken in each division.
The chance the late flight is full is 0.7. The chance both flights are full is 0.6. Can we believe the two flights being full are independent events?
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