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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.
a social psychologist was interested in examining the effect of being observed on sports performance and if competition
Construct a 95% confidence interval for the difference M1-M2 between the mean spending on prescription allergy relief medication (M1).
The following data were obtained in an experiment to estimate a possible relation between the number of showings in one week of a TV commercial in typical sales territories and the sales (in thousands of units) in that territory of the advertised ..
Apply the EOQ model to the following quantity discount situation in which D=500 units per year, C0=$40, and the annual holding cost rate is 20%. What order quantity do you recommend?
christine is currently taking college astronomy. the instructor often gives quizzes. on the past seven quizzes
Would this indicate that the actual proportion of stopped drivers given tickets is not equal to .88? Use a 1% significance level.
Create the acceptance-rejection technique for creating the geometric random variable, X, with parameter p on range {0, 1, 2, ...}.
A person's body temperature is found to be 101.00 °F. Is the result unusual? Why or why not? What should you conclude? What body temperature is the 95th percentile?
The ancient Greeks thought that the most pleasing shape for a rectangle was one for which the ratio of the length to the width was 8 to 5, the golden ration.
In recent years, fishermen have suffered financial hardship because of shortened fishing seasons, reduced catches and lower market prices. Moreover, fishermen have complained about price fluctuations and have called for a system of minimum prices.
The data follow. Males Females 27 25 25 29 19 18 10 23 16 20 22 15 14 19 (a) What statistical test should be used to analyze these data?
If f is upper semicontinuous on a compact space S, show that for some t ∈ S, f (t ) = sup f := sup{ f (x ): x ∈ S}. Hint: Let an ∈ R, an ↑ sup f . Consider f -1((-∞, an )), n = 1, 2,... .
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