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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 |.
Past studies indicate that only 85% of booked passengers show up for their flight. Find the probability that if the airline books 150 persons for a 140-seat plane, not enough seats will be available.
Determine a forecast for the average weekly sales in year 5 for each of the three seasons.
If a player bets a dollar on black, and if the ball stops on a black number, he gets his dollar back and another dollar. If the ball stops on a red number or on 0 or 00 he loses his dollar. Find the expected winnings for this bet.
Construct a scatterplot for the (x, y) values below, and answer the following questions. What would be the slope of this regression line?
Assignment Objectives: Construct a scatter plot for two variables, Compute the correlation coefficient, Compute the formula for the regression equation
Let S be any set and S∞ the set of all sequences {xn }n≥1 with xn ∈ S for all n. Let C be a subset of the Cartesian product S × S∞. Also, S × S∞ is the set of all sequences {xn }n≥0 with xn ∈ S for all n = 0, 1,... .
estimating the sample standard deviation using normal score.for a sample with a mean of m 85 a score of x 90
the fox tv network is considering replacing one of its prime-time crime investigation shows with a new family-oriented
A random sample of 36 customers is selected. What is the probability that the average time spent per customer is between 2.9 and 3.2 minutes?
Recent studies have shown that the super-cooling temperature of terrestrial frogs frozen at -6°C has a relative frequency distribution with a mean of - 2°C and a standard deviation of 0.3°C (The first of these studies was reported in Science, May ..
A statistics professor plans classes so carefully that the lenths of her class are uniformly distributed between 50.0 and 52.0 minutes. Find the probability that a given class period runs less than 51.5.
A sample of 350 hats is selected and the sample mean is 3.25 pounds. Using a level of significance of .10, is there evidence that the population mean weight of the hats is greater than 3.5 pounds? Fully explain your answer.
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