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1. In any infinite-dimensional F -space, show that any compact set has empty interior.
2. A continuous linear operator T from one Banach space X into another one Y is called compact iff T {x ∈ X : lx l≤ 1} has compact closure. Show that if X and Y are infinite-dimensional, then T cannot be onto Y . Hint: Apply Problem 10.
3. Show that there is a separable Banach space X and a compact linear operator T from X into itself such that T {x : lx l ≤ 1} is not compact. Hint: Let X = c0, the space of all sequences converging to 0, with norm l{xn }l := supn |xn |.
In your environment (business or personal), please describe a hypothesis test related to a decision. What would be your data? What would be your null hypothesis? What would be your alternate hypothesis? What would be your Type 1 and Type 2 errors ..
Determine future value of annuity due which has $750 deposited at the starting of each month for 15 years at 5.9% compounded monthly.
Problem on standard deviation
Find P-Value with 0.05 significance level, and state the conclusion about the null hypotheses (reject or fail to reject) With H1: p is not equal to 3/4, the test statistic is z=0.35
The experiment data in below table was to evaluate the effects of three variables on invoice errors for a company. Invoice errors had been a major contributor to lengthening the time that customers took to pay their invoices and increasing the acc..
You're responsible for planning parking needed for a new 256-unit apartment complex, and you're told to base the needs on the statistic 'average number of vehicles per household is 1.9'.
q1. a furniture store expects to sell 640 sofas at a steady rate next year. the manager of the store plans to order
at a large university it is known that 40 of the students live on campus. the director of student life is going to take
in a sample of discharge of suspended solids from a phosphate mine it was noted that the mean daily discharge was 27
Normal distribution with a mean of 33 oz. and a standard deviation of 0.7 oz. What proportion of packets are underweight (i.e., weigh less than 32 oz.)?
suppose you are interested in bidding on a piece of land and you know that one other bidder is interested. the seller
q1. when do americans decide what to make for dinner? an outline survey indicated that 74 of americans decided either
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