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8. (a) Let Q be the set of rational numbers. Show that the Riemann integral of 1Q from 0 to 1 is undefined (the net in its definition does not converge). (Q is countable and [0, 1] is uncountable, so the integral "should be" 0, and will be for the Lebesgue integral, to be defined in Chapter 3.)
(b) Show that for a sequence 1F (n) of indicator functions of finite sets F (n) converging pointwise to 1Q, the Riemann integral of 1F (n) is 0 for each n.
9. Let X be an infinite set. Let T consist of the empty set and all complements of finite subsets of X . Show that T is a topology in which every singleton {x } is closed, but T is not metrizable. Hint: A sequence of distinct points converges to every point.
At the .10 level of significance, is the coin biased toward heads? Show your decision rule and calculations. (b) Calculate a p-value and interpret it.
calculate a 99 confidence interval for the true mean of a bearings diameter when a sample of 16 of the bearings have a
Discuss various types of two dimensional diagrams. Explain with Ex., how these are prepared? Distinguish between Natura.I scale and Ratio Scale What are the methods of constructing graphs on ratio scale?
3 methods, A, B, and C are available for teaching a certain industrial skill. Only one of these methods is used in teaching a particular worker.
If μ represents the mean increase in the verbal SAT score if all high school students used the method, the alternative hypothesis the teacher wishes to test is what?
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Calculate the value based on this information. A new screening test for Lyme disease is developed for use in the general population. The sensitivity (ability to identify infected persons) is 60% and specificity (ability to identify non- infected p..
A start-up publishing company estimates that the fixed costs of its first major project will be $190,000, the variable cost will be $18, and the selling price per book will be $34.
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Draw a scatterplot indicating a strong negative relationship between the variables pf income and mental illness. Be sure to label the axes correctly.
a student observes the elevator usage of a building with a single elevator. this elevator will only allow people to go
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