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Question: We are continually hearing reports on the nightly news about natural disasters-droughts in Texas, hurricanes in Florida, floods in California, and so on. We often hear that one of these was the "worst in over 30 years," or some such statement. Are natural disasters getting worse these days, or does it just appear so? How might you use simulation to answer this question? Here isone possible approach. Imagine that there are N areas of the country (or the world) that tend to have, to some extent, various types of weather phenomena each year. For example, hurricanes are always a potential problem for Florida, and fires are always a potential problem in southern California. You might model the severity of the problem for any area in any year by a normally distributed random number with mean 0 and standard deviation 1, where negative values are interpreted as good years and positive values are interpreted as bad years. (We suggest the normal distribution, but there is no reason other distributions couldn't be used instead.) Then you could simulate such values for all areas over a period of several years and keep track, say, of whether any of the areas have worse conditions in the current year than they have had in the past several years, where "several" could be 10, 20, 30, or any other number of years you want to test. What might you keep track of? How might you interpret your results?
Now, suppose that the company currently has 180 units in stock, and it will not be receiving any further shipments from its supplier for at least 3 weeks. What is the probability that the company will run out of units
(a) If F : R^n → R^m is a linear transformation and n > m then there exists a nonzero vector x such that F (x) = 0. (b) If F : R^n → R^m and G : R^k → R^n are linear transformations such that ker F = {0} and ker G = {0} then ker F ? G = {0}.
Calculate the exact 95 percent upper and lower confidence limits for the population mean of LOS. Calculate the exact 95 percent upper and lower confidence limits for the population mean of charges
A chemist needs 150 milliliters of a 23% solution but has only 12% and 27% solutions available. Find how many milliliters of each should be mixed to get the desired solution.
Prob1. LetT∈L(V,W).Prove (a) T is injective if and only if T ∗ is surjective; (b) T ∗ is injective if and only if T is surjective.
Programmers often choose Bézier surfaces for applications (such as an airplane cockpit simulator) that require real-time rendering.
Solve problem of the Rhind Mathematical Papyrus by the method of false position : A quantity and its 2 are added together and from the sum 1 of the sum is subtracted 3 3 and 10 remains. What is the quantity?
Explain why extra capacity can be valuable even though the company already has more total capacity than it requires.
In 2001, 400 seat Boeing 747s were priced at $200 million each, 300 seat Boeing 777s were priced at $160 million, and 200 passenger Airbus A321s were priced at $60 million.
Can you use the well-ordering property to prove the statement: "Every positive integer can be described using no more than fifteen English words"?
You will write a Riemann sum approximating a definite integral and use a computer algebra system to find a formula for the Riemann sum.
Galileo was the first person to show that the distance traveled by a body falling from rest is proportional to the square of the time it has traveled.
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