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For a finite measure space (X, S, µ), a set F of integrable functions is said to be uniformly integrable iff sup{( | f | dµ: f ∈ F } <>∞ and for every ε > 0, there is a δ > 0 such that if µ( A) <>δ, then (A | f | dµ <>ε for every f ∈ F . Prove that a sequence { fn } of integrable functions satisfies ( | fn - f | dµ → 0 if and only if both fn → f in measure and the fn are uniformly integrable.
let x and y be independent exponential random variables with means 2 and 3 respectively. let zxy. determine
Write a short report dicussing the claim that average diastolic blood pressure in 1958 (variable dbp58) is the same for men who were alive in 1968 and for men who were not.
an srs of 40 san diego county schools graduates showed that 26 of the 40 enrolled in a college or university right out
A sample of 4 axles is inspected each hour for process control purposes, and records are kept of the sample mean diameter. What will be the mean and the standard deviation of the numbers record.
Stating assumptions on which your arguments and conclusions are based, sum up the statistical evidence regarding effectiveness of this diet.
what is the probability that a well shuffled deck will produce a straight flush five cards of one suit in order akqj10
What are the implications for building a requisite model of the current car-purchase decision if trading in the car is treated as an uncertain event? As a decision?
Define validity and reliability. How can we insure our data is both reliable and valid? Which of these two do you think is the more important?
Estimate, with 95% confidence, the actual average settlement time (in days) for claims received by the Explorer Fund only. Interpret the result.
among the 15 scientists working on a research project 10 have ph.d.s. if four of these scientists are chosen at random
suppose you are an art dealer. you specialize in buying paintings by unknown painters at auctions and re-selling them
A pizza restaurant manager claims that the average home delivery time for their pizza is no more than 20 minutes.
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