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Let (S, T ) be a second-countable topological space and (Y, d) any metric space. Show that the Borel σ-algebra in the product S × Y is the product σ-algebra of the Borel σ-algebras in S and in X. Hint: This improves on Proposition 4.1.7. Let V be any open set in S × Y . Let {Um }m≥1 be a countable base for T . For each m and r > 0 let Vmr := {y ∈ Y : for some δ > 0, Um × B(y, r + δ) ⊂ V } where B(y, t ) := {v ∈ Y : d(y, v) <>t }. Show that each Vmr is open in Y and V = lm,n Um × Vm,1/n.
post cereals has decided to run a promotion whereby they are putting 10 different yu-gi-oh cards in specially marked
Four are slow songs, and six are fast songs. Each song is to be played only once. In how many ways can the disc jockey play the 10 songs if. The songs can be played in any order.
a businessman has two independent investments a and b available to him but he lacks the capital to undertake both of
A study of cardiovascular risk factors compared heavy smokers, light smokers, and nonsmokers. Both men and women were included in the study and gender differences were also to be investigated. One of the variables measured was the heart rate after..
The next table shows the results of this independent t-test. At the .05 significance level, can we conclude that there is a difference in their mean times? Explain these results to a person who knows about the t test for a single sample but is unf..
A quality inspector is interested in the time spent replacing defective parts in one of the company's products. The average time spent should be at most 20 minutes per day according to company standards.
Second treatment had M = 52 with s^2 = 36. Do these data point to significant difference between two treatments? Use the two-tailed test with α = .05.
Although the packet claims a germination rate of 92%, only 171 or 200 test seeds sprout. Is this evidence that the seeds have lost viability during a year in storage?
a certain airplane has two independent alternators to provide electrical power. the probability that a given alternator
a citrus farmer has determined that the diameter of its grapefruits are normally distributed with a mean of 4.5 inches
question probability and statistical qualityq1. an unbiased coin is tossed twice. calculate the probability of each of
Should the engineering firm be concerned? Perform an appropriate hypothesis test, showing the necessary calculations and/or explaining the process used to obtain the results.
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