Discussion about the symmetry under rotations

Reference no: EM131811791

Question: Symmetry under rotations.

a) Suppose the joint distribution of X and Y is symmetric under rotations, Are X and Y necessarily independent? Are they necessarily uncorrelated? Explain by arguments or examples.

b) Suppose (X, Y) is a point picked at random from the unit circle X² + Y² = 1, Calculate E(X²), E(Y²), and E(XY).

c) Suppose U is uniformly distributed on (0, 1), X = Cos 2πU, Y = Sin 2πU. Are X and Y uncorrelated? Are X and Y independent? Explain carefully the connection between b) and c).

Reference no: EM131811791

Questions Cloud

Determine the equivalent units for june : 1. Determine the equivalent units for June for the Blending Department.

Reflect upon how the ideas of certain philosophers influence : Reflect upon how the ideas of certain philosophers influenced literary works produced during the Enlightenment and Modern literary periods.

Calculate the net advantage of closing : Calculate the net advantage of closing the North Store. (Any losses should be indicated by a minus sign.)

What total should roses balance sheet include : This subsidiary's functional currency is a foreign currency. What total should Roses balance sheet include for the preceding items

Discussion about the symmetry under rotations : Suppose the joint distribution of X and Y is symmetric under rotations, Are X and Y necessarily independent? Are they necessarily uncorrelated?

Compute the equivalent units of materials : 1. Compute the equivalent units of materials, labor, and overhead in the ending inventory for the month.

Write an essay about brooke gladstone and josh neufeld : Write an essay about Brooke Gladstone and Josh Neufeld, The Influencing Machines and Kevin Kelly, Better than Human: Why Robots Will - and Must- Take Our Jobs.

What is the chance that they all major in accounting : Suppose 30% of business majors major in accounting. You take a random sample of 3 business majors.

What is the balance in work in process inventory on december : The cost of goods manufactured was $220,000 in 2011. What is the balance in work in process inventory on December 31, 2011? $24,000

User Account

All Pages