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Question: The Board of Directors of the company, having the hierarchy structure, was disheartened at the revelation that 50% of its employees at upper levels of management were incompetent. The Board therefore engaged the services of two management consulting firms to seek advice on how to improve the situation. One firm suggested that the promotion policies be tightened up to avoid promoting incompetents. They outlined a program of regular interviews, testing, and peer evaluation that they claimed would screen out essentially all incompetents from promotion. (In our terms this proposal would change P by replacing the element in the lower right corner by zero.)
The second consulting firm suggested that the screening was already adequate, but that what was required was the initiation of employee training. They outlined a program of motivation enhancement, internal courses, and so forth. They estimated that, with a modest effort, they could increase the number of incompetents who become competent at their job over a one-year period from the present rate of one out of eight to a rate of two out of eight. They argued that such a program would significantly affect the quality of the upper levels. If both proposals were about equally costly to implement, which should the Board select? Will either plan drastically affect the ratio of the number of people at successive levels (near the top)?
Dirichlet series
Every convergent sequence contains either an increasing, or a decreasing subsequence.
How many relations on A are both symmetric and antisymmetric?
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This question is asking you to compare the likelihood of your getting 4 or more subscribers in a sample of 50 when the probability of a subscription has risen from 0.02 to 0.06.] Talk about the comparison of probabilities in your explanation.
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Suppose that in the four player game, the person who rolls the smallest number pays $5.00 to the person who rolls the largest number. Calculate each player's expected gain after one round.
Find the probability density function.
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