Attainment of monge-wasserstein distances

Assignment Help Basic Statistics

Reference no: EM13990659

Show that there exist three laws α, β, and γ on R2 such that there is no law P on R6 with coordinates x, y, and z in R2 for which x, y, and z have laws α, β, and γ , respectively, and E |x - y|= W (α, β), E |y - z|= W (β, γ ), and E |x - z|= W (α, γ ). Hint: Let a, b, and c be the vertices of an equilateral triangle of side 1. Let α := (δa + δb )/2,β = (δa + δc )/2, and γ = (δb + δc )/2. (So the simultaneous attainment of Monge-Wasserstein distances by random variables for all laws, as in R1 in Problem 2, no longer is possible in R2.)

Reference no: EM13990659

Questions Cloud

How much energy needed to light a loo watt bulb for a minute : What does it cost if you leave a 100 watt light bulb on overnight ? One horse-power is about 750 watts. How many horsepower is a 10 kwatt motor ?

The atmospheric pressure varies with height : The atmospheric pressure varies with height according to the following barometric formula: P = Pgas x e (-gMh/RT)

Sodium amide : Sodium amide, NaNH2, is a salt that contains the very strong base, amide ion (NH2-). Considering the fact that amide ion is a much stronger base than hydroxide ion, OH-, describe what will happen when sodium amide is dissolved in water.

Calculate the amount of interest : A $40,000 loan at 4% dated June 10 is due to be paid on October 11. Calculate the amount of interest

Attainment of monge-wasserstein distances : Let a, b, and c be the vertices of an equilateral triangle of side 1. Let α := (δa + δb )/2,β = (δa + δc )/2, and γ = (δb + δc )/2. (So the simultaneous attainment of Monge-Wasserstein distances by random variables for all laws, as in R1 in Proble..

How computerized accounting systems impact internal control : Post on the Discussion Board a summary of the company and its objectives for the implementation. Do not just post a transcript of your interview, but synthesize the responses into a well written case study.

Describe the difference between mentoring and coaching : Describe the difference between mentoring and coaching - Identify your customers and improve your understanding of their needs, what are 5 questions you should ask yourself?

Inverse of the distribution function : 1. Show that if S is the real line R with usual metric, then Theorem 11.7.2 holds for the probability space (0, 1) with Lebesgue measure. Hint: Let Xn be the inverse of the distribution function of Pn as defined in Proposi- tion 9.1.2.

How many people can be lifted one story with a megajoule : What is the force of gravity on a 1 kg mass ? What energy is needed to lift a 1 kg mass a distance of 3 meters ? What energy is needed to lift you one story in this building ?

User Account

All Pages