Correlation with two independent variables

rhuelu
Messages
17
Reaction score
0
I would appreciate some help with this problem. Assuming X and Y are independent, I'm trying to find the correlation between XY and Y in terms of the means and standard deviations of X and Y. I'm not sure how to simplify cov(XY,Y)=E(XYY)-E(XY)E(Y)
=E(XY^2)-E(X)E(Y)^2.

If X and Y are independent, does it follow that X and Y^2 are independent. If this is the case, then covariance is zero --> correlation is zero. If this isn't the case I'm really not sure how to proceed. Any help is appreciated...
 
Physics news on Phys.org


rhuelu said:
I would appreciate some help with this problem. Assuming X and Y are independent, I'm trying to find the correlation between XY and Y in terms of the means and standard deviations of X and Y. I'm not sure how to simplify cov(XY,Y)=E(XYY)-E(XY)E(Y)
=E(XY^2)-E(X)E(Y)^2.

If X and Y are independent, does it follow that X and Y^2 are independent.
yes.
If this is the case, then covariance is zero --> correlation is zero. If this isn't the case I'm really not sure how to proceed. Any help is appreciated...
 


how would you prove this?
 


rhuelu said:
how would you prove this?

what do you mean by "independent"?
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

Calculate the correlation coefficient in the given problem
Replies
7
Views
1K
How to determine if random variables x,y,z are independent?
Replies
3
Views
2K
Are X and Y dependent random variables?
Replies
1
Views
1K
Determine the mean square error of a simple distribution
Replies
4
Views
1K
Independence of Random Variables
Replies
6
Views
2K
Signal Processing: Finding the auto-correlation
Replies
2
Views
2K
Calculating the covariance of two discrete random variables
Replies
2
Views
1K
Finding the flow of a vector field
Replies
5
Views
2K
Question on Two Differentiation Techniques
Replies
25
Views
2K
Finding Probability Density Functions for Independent Random Variables
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top