Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. statistics
  3. 1. can two variables share a deterministic relatio

1. Can two variables share a deterministic relationship, and yet be uncorrelated? For instance, suppose that X...

60.1K

Verified Solution

Question

Statistics


1. Cantwo variables share a deterministic relationship, and yet beuncorrelated? For instance, suppose that X follows a continuous,uniform distribution between −1 and 1:
X ~U[−1, 1].
a.Draw a graph of the distribution of X.
By asymmetry argument—the distribution of X is symmetric around zero—itis clear that E(X) = 0.
Nowlet Y = X2.
b.Clearly Y and X are not independent; in fact, a deterministicrelationship exists between them (if you know X, you know Y). Show,however, that X and Y are uncorrelated: Cov(X,Y) = 0. Hint: use asymmetry argument for the distribution of X3.
c. Canyou explain why there is no correlation despite an obviousrelationship?

Answer & Explanation Solved by verified expert
4.0 Ratings (403 Votes)
    See Answer
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students

Statistics
1.2K views

STUDY 4 The university is building a number of active learning classrooms and came across a chair...

Psychology
1.2K views

Discuss the controversy over female abilities for math and/or science. How do females typically fare in...

Physics
1.2K views

Three moles of an ideal monoatomic gas performs a cyclic process as shown in the...

Physics
1.2K views

FL Fo 1 Fox Calculate the net work done by the force F whose variation...

Statistics
1.2K views

Consider the chart below of living arrangements. ...

Calculus
1.2K views

The range R of a projectile is related to the initial velocity v and projection...

Accounting
1.2K views

(2) Expected payments for landacipingsuppliss. (b) Determine the following...

Accounting
1.2K views

BRIEF EXERCISE 6-5 Understanding Cost Behaviour and Contribution Margin [LO1 - CC1, 3; LO3 -...

Accounting
1.2K views

Tim Marlow, the owner of The Clock Works, wanted to know how many clocks he...

Accounting
1.2K views

Which of the following would be included in the cost of a product manufactured according...

Finance
1.2K views

50 YEARS OF ELECTROMOBILITY: PIONEER AND DRIVER OF INNOVATION. The visionary history of electric BMW...

Finance
1.2K views

Your costs per buildable SF are Hard Costs of $70psf, Soft Costs of $20psf, and...