Explore BrainMass
Share

Statistics: Joint, marginal and conditional densities & expectation

This content was STOLEN from BrainMass.com - View the original, and get the already-completed solution here!

** Please see the attached file for a Word formatted copy of the problem **

1. Consider the joint pmf p(x,y)=cxy, 1<x<y<3.
a) Find the normalizing constant c.
b) Are X and Y independent? Prove your claim.
c) Find the expectations of X, Y, XY.

2. Conceptual
Suppose (X, Y) have the joint pmf p(x, x+1) = 1/(n+1), x= 0,1,2,.....,n.
a) Are X, Y independent?
b) What is E( YlX = x)?
c) What is Var( YlX=x)?
d) What is Var(X)?
e) What is Var(Y-X)?

3. X, Y are jointly distributed Uniformly within the Unit circle. What is, the joint PDF is
f(x,y) = c, if X2+Y2 < 1
=0, otherwise.
a) Are X,Y independent?
b) Find the marginal PDF of X.
c) Find E(X).
d) Find E(Y).
e) Find E(X-Y).
f) Find Var(X-Y).

4. (expectation of a Quotient) suppose X and Y are independent and X~Be(2,2), Y~Be(3,3). Find E(X2/Y2).

© BrainMass Inc. brainmass.com October 17, 2018, 2:44 am ad1c9bdddf
https://brainmass.com/statistics/probability/joint-marginal-conditional-densities-expectation-393921

Attachments

Solution Summary

This solution provides a step-by-step tutorial showing how to compute the given probability questions.

$2.19
Similar Posting

Statistical Methods

I am in a peer/mentor group. We are meeting to discuss statistical methods. I need to discuss the goals of two statistical methods.

The statistical methods are to be selected by you. What are some statistical methods? What does each method attempt to accomplish? I only need to address two.

View Full Posting Details