Register to reply

Conditional Expectation, change of variables, change of variables, CharacteristicsFcn

Share this thread:
kliwin
#1
Nov21-12, 01:10 AM
P: 1
1.
Let T = (X,Y,Z) be a Gaussian for which X,Y,Z for which X, Y, Z are standard normals, such that E[XY] = E[YZ] = E[XZ] = 1/2.

A) Calculate the characteristics function Φ_T(u,v,w) of T.
B) Calculate the density of T.

2.
Let X and Y be N(0,1) (standard normals), not necessarily independent. Calculate E[Max(X,Y)] using two different ways:

A) Use the joint density of X and Y and use the fact that for two numbers x and y, max(x,y) = x if x > y and y if y > x.

B) Use the change of variables x = x and y = ρx = u*sqrt(1-ρ^2) in your integral.

3.
Given random variables X and Y whose second moments exit, prove the triangle inequality

E[(X+Y)^2]^(1/2) <= E[X^2]^(1/2) + E[Y^2]^(1/2)

Help guys, this is for my Advanced Probability Course and I am stuck on it. :/
Phys.Org News Partner Science news on Phys.org
World's largest solar boat on Greek prehistoric mission
Google searches hold key to future market crashes
Mineral magic? Common mineral capable of making and breaking bonds

Register to reply

Related Discussions
Conditional expectation of a product of two independent random variables Calculus & Beyond Homework 0
Using change of variables to change PDE to form with no second order derivatives Calculus & Beyond Homework 1
Conditional expectation on multiple variables Set Theory, Logic, Probability, Statistics 2
Expectation conditional on the sum of two random variables Calculus & Beyond Homework 0
3D Change of Variables Calculus & Beyond Homework 2