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1. Show that in any finite dimensional Banach space (Rk with any norm), for any closed, convex set C and any point x not in C , there is at least one nearest point y in C ; in other words, ly - x l= infz∈C lz - x l.
2. Give an example of a closed, convex set C in a Banach space S and an x ∈ S which has no nearest point in C . Hint: Let S be the space £1 of absolutely summable sequences with norm l{xn }l1 := },n |xn |. Let C := {{t j (1 + j )/j } j ≥1: t j ≥ 0, }, j t j = 1} and x = 0.
Assume that 13 % of the population of the U.S. is left-handed. If a random sample of 180 people from the U.S. is chosen, approximate the probability that fewer than 26 are left-handed.
a study of 200 computer service firms revealed these incomes after taxesincome after taxesnumber of firmsunder 1
What is the 95% Confidence Interval for the true population slope between Wins and Saves and what is the standard error of the estimate and what are its units?
out of 10 trials a receiver got four cards correct. what is her success rate? what is her expected rate of success
A simple random sample of 120 orders will be used to estimate the porportion of first time consumers. Assume he is correct. What is the sampling distribution of p for the study?
q1. for this assignment you will be provided with 2 clinical research questions on sample size and one published
the manager of sandy corporation wants to determine whether or not the type of work schedule for her employees has any
the transportation safety authority tsa has developed a new test to detect large amounts of liquid in luggage bags.
We often hear you can lie with statistics. This is one way of saying statistics can be easily mis-communicated. Find one example of how statistics are mis-communicated and explain why there was a mis-communication and what you would do to correct ..
customers arrive at a checkout counter in a department store according to a poisson distribution at an average of
Chocolate chip cookies resulted in the following calorie amounts. At the a _ 0.01 level, is there sufficient evidence that the average calorie content is greater than 110 calories?
Ssample by constructing a histogram and finding the sample mean and standard deviation, are we investigating the sampling distribution of the mean? why or why not?
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