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1. Give an example of a set A in R2 which is radial at every point of the interval {(x, 0): |x | 1} but such that this interval is not included in the interior of A.
2. Show that the ellipsoid x 2/a2 + y2/b2 + z2/c2 ≤ 1 is convex. Find a support plane at each point of its boundary and show that it is unique.
3. In R3, which planes through the origin are support planes of the unit cube [0, 1]3? Find all the support planes of the cube.
4. The Banach space c0 of all sequences of real numbers converging to 0 has the norm I{xn }I := supn |xn |. Show that each support hyperplane H at a point x of the boundary ∂ B of the unit ball B := {y: IyI ≤ 1} also contains other points of ∂ B. Hint: See Problem 7 of §6.1.
if the age of an initial cardiac incident heart attack or sudden cardiac arrest is normally distributed with a
assume that matched pairs of data result in the given number of signs when the value of the second variable is
what is the distribution of the case described here? mr. hr hits a homerun in his turn at a baseball game with 5 of
calls to the help line of a large computer distributor follow a passion distribution with a mean of 20 calls per
The standard deviation of test scores on a certain achievement test is 11.3. If a random sample of 81 students had a sample mean score of 74.6, find a 90 percent confidence interval estimate for the average score of all students.
Poisson distribution with a mean of 8.8 tickets per day. Find the probability that less than six tickets are written in one hour given that the police works for 12 hours.
Assume that a population is normally distributed with a mean of 100 and a standard deviation of 15. Would it be unusual for the mean of a sample of 3 to be 115 or more? Why or why not?
Suppose the people living in a city have a mean score of 48 and a standard deviation score of 7 on a measure of concerns about the environment.
Determine the critical value, z0, to test the claim about the population proportion p
1. if x is a binomial random variable with parameters n and p show that y n?x is also a binomial random variable. what
Suppose the people have weights that are normally distributed with a mean of 164lb and a standard deviation of 30lb. Find the probability?
question during may a certain drawbrige over the intercoastal waterway is raised every half hour to allow boats to
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