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1. Let (X, d) and (Y, e) be pseudometric spaces with topologies Td and Te metrized by d and e respectively. Let f be a function from X into Y. Show that the following are equivalent (as stated in the first paragraph of this chapter):
(a) f is continuous: f -1(U ) ∈ Td for all U ∈ Te .
(b) f is sequentially continuous: for every x ∈ X and every sequence xn → x for d, we have f (xn ) → f (x ) for e.
2. Let (S, d) be a metric space and X a subset of S. Let the restriction of d to X × X also be called d. Show that the topology on X metrized by d is the same as the relative topology of the topology metrized by d on S.
negligent treatment-caused injury
Garbage quantity is approximately normally distributed. Find the probability that the mean from a sample of 30 families will have between 17 and 18 pounds of garbage.
The production manager for Beer etc. produces 2 kinds of beer: light and dark.
For random samples of size n = 25 selected from a normal distribution with a mean of m = 50 and a standard deviation of s =20, find each of the following: The range of sample means that defines the middle 95% of the distribution of sample means.
a recent report indicated an average family of four 2 parents and 2 children under the age of 16 spends 500 per month
If the rules are now altered so that Carol returns her card to the pack after noting its value, and also, if Carol and David draw the same card all the cards are shuffled and they draw again.
Write 1-2 paragraphs for each component of the model (days-to-repair; interval between breakdowns; lost revenue; putting it together).
A component has an exponential time-to-failure distribution with a mean of 10,000 hours. The component has already been in operation for its mean life. What's the probability that it will fail by 15,000 hours?
you are testing whether there is a significant difference in the proportions of college students and similar aged non college students having accidents during the two year period. What is the value of your pooled proportion?
Suppose a new weight loss program was sponsored by the local health and fitness club in a small town. The program claims to make people lose more than five pounds in a month. Twelve participants were selected and their weights were recorded.
Let A be the event that a student is enrolled in an accounting course, and let S be the event that a student is enrolled in a statistics course.
Discuss the various forms of disclosure available in published financial statements.
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