Statistics: Joint, marginal and conditional densities & expectation
Not what you're looking for?
** 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).
Purchase this Solution
Solution Summary
This solution provides a step-by-step tutorial showing how to compute the given probability questions.
Purchase this Solution
Free BrainMass Quizzes
Know Your Statistical Concepts
Each question is a choice-summary multiple choice question that presents you with a statistical concept and then 4 numbered statements. You must decide which (if any) of the numbered statements is/are true as they relate to the statistical concept.
Terms and Definitions for Statistics
This quiz covers basic terms and definitions of statistics.
Measures of Central Tendency
Tests knowledge of the three main measures of central tendency, including some simple calculation questions.
Measures of Central Tendency
This quiz evaluates the students understanding of the measures of central tendency seen in statistics. This quiz is specifically designed to incorporate the measures of central tendency as they relate to psychological research.