the last two are kind of giving me problems so if anyone has any ideas, I'd really appreciate it. 4. Let d₁ and d2 be metrics on sets X and Y respectively. Prove that(i) d is a metric on X x Y, whered((x1, y₁), (x2, y2)) = max{d₁(x1, x2), d2(y₁, y2)}.(ii) e is a metric on X x Y, wheree((x1, y₁), (x2, y2)) = d₁(x₁, x2)+d2(y1, y2).(iii) d and e are equivalent metrics.

To show that e is metric on X×Y we have to prove three property a) non-negativity b) symmetry c)…

Answered: 4. Let d₁ and d2 be metrics on sets X…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A researcher is interested in whether people who enjoy fine wine can actually tell the difference between a highly rated expensive wine and a good inexpensive wine. She selects several bottles of a highly rated cabernet sauvignon (a red wine) costing over $100 per bottle and several bottles of a good cabernet sauvignon costing $12. Subjects will taste a glass of wine without knowing whether it is the expensive or inexpensive wine. This is the treatment. They will then be asked to estimate how much the wine cost. This is the response variable. Outline a completely randomized design to compare the cost estimates for the two treatments. Twenty subjects are available. Group 1 Treatment 1 10 subjects expensive wine Compare Price estimate Random assignment Treatment 2 A Grouo 2 10 subjects inexpensive wine Group 1 10 subjects - expensive wine Random assignment Compare price estimates Group 2 10 subjects - inexpensive wine Treatment 1 Group 1 20 subjects expensive wine Compare Price estimate…
please see the attached question. thanks for your help
Netflix made headlines in September 2011 when it split its streaming video service and its DVD by-mail service into two companies. This decision was based on projections that streaming videos will replace DVDs in the future. In this problem, you will explore these projections. Numbers below are close to the correct values, but vary to allow more practice with this idea. Total DVD and Blu-ray disc sales in 2009 were $8.72 billion. For the purposes of this problem, you will combine DVD and Blue-ray disk sales into one category of DVD sales. A study by In-Stat predicted that "physical disc sales will decline by $4.7 billion by 2014," and that "streaming, on the other hand, should grow from its current $2.1 billion to $6.3 billion over the same time period (2009–2014)." What is the slope, including units, of the model for streaming videos?
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4. Let d₁ and d2 be metrics on sets X and Y respectively. Prove that (i) d is a metric on X x Y, where d((x1, y1), (x2, y2)) = max{d₁(x1, x2), d2(y1, y2)}. (ii) e is a metric on X x Y, where e((x1, y₁), (x2, y2)) = d₁(x1, x2)+d2(y1, 32). (iii) d and e are equivalent metrics.