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1. Take the Cantor function g defined in the proof of Proposition 4.2.1. As a nondecreasing function, it defines a measure ν on [0, 1] with ν((a, b]) = g(b) - g(a) for 0 ≤ a b ≤ 1 by Theorem 3.2.6. Show that ν ⊥ λ where λ is Lebesgue measure.
2. In [0, 1] with Borel σ-algebra B, let µ( A) = 0 for all A ∈ B of first cate- gory and µ( A) = +∞ for all other A ∈ B. Show that µ is a measure, and that if ν is a finite measure on B absolutely continuous with respect to µ, then ν ≡ 0. Hint: See §3.4, Problems 7-8. Thus, the conclusion of the Radon-Nikodym theorem holds with h ≡ 0, although µ is not σ-finite.
compute the standard error of the estimate of the data below.x values 41 55 61 68 82y values
Many people believe that abnormal behavior is more likely to occur during a full moon. As a test for empirical evidence to support this belief, a study was conducted based on admission of new clients over a one year period by lunar phases:
Calculate the correlation between decorating and Christmas enjoyment - Maximize Wayne's studying effectiveness.
a sample of eight mother daughter pairs of subjects was obtained and their heights in inches were measured. the linear
The breaking strengths of cables produced by a certain manufacturer have a mean, of 1925 pounds, and a standard deviation of 65 pounds. It is claimed that an improvement in the manufacturing process has increased the mean breaking strength.
question over a period of years a toothpaste has received a mean rating of 5.9 on a 7-pointscalefor overall customer
Conduct an analysis of four management journal articles, at least two of which must be peer reviewed. The following must be included in my analysis:
an insurance company receives 100 claims per day on average. claims arrive independently and at random at the company
Why do we care whether the assumptions required for statistical tests are met? (Tip: You might also want to write your answer on a note card you paste to your computer.)
Find a 95% confidence interval for the mean weight of the population of all such runners, assuming that the population standard deviation is o=4.5 kg. Based on the confidence interval, does a test of Ho: u=61.3kg, Ha: u =/ 61.3kg
if you take the within groups sum of squares and divide it by the between groups degrees of freedom you getthe mean
Show that there is a continuous function from [0, 1] onto Tin≥1[0, 1]n , a countable product of copies of [0, 1], with product topology. Hint: Take the sequence f (k) as in Problem 10. Let Fk (t )n := f (k)(t )n for n ≤ k, 0 for n > k. Show that F..
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