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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.
suppose that from the past experience a professor knows that the test score of a student taking his final examination
At 95% confidence using the critical value approach, test to see if the percentage of defective systems produced by x-Game has exceeded the industry standard.
Suppose the budget has the support of 53% of voters. What is the probability that the newspaper's sample will lead it to predict defeat? The probability is...........round to 2dp.
Find the P-value that would be used to determine if the percentage of customers who prefer mint chocolate chip ice has increased at a 5% level of significance.
the lifetimes of light bulbs of a particular type are normally distributed with a mean of 280 hours and a standard
Write methods that accept an array or list and returns lowest score, highest score, median score, average score and the standard deviation of the scores.
Welcome a woman taking the initiative in asking for a date. What is the probability that seven (7) of the men say NO.
The following random sample was collected: 22 33 44 6 The 80% confidence interval for the mean is?
Douglas Boats is a supplier of boating equipment for the states of Oregon and Washington.
Find the t value for 5, 2.5, and 0.5% of the area within each tail for a sample size, n, that is very large or infinite. How do these t values compare with corresponding z values?
suppose that for a set of numeric data we have the following sample statisticsx with bar on top equal 10y with bar on
There is one Grand Prize of $500, one First Prize of $100, and 8 Second Prizes of $50. Find the expected winnings per ticket sold.
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