Results 1 to 5 of 5

Math Help - Covariance and correlation

  1. #1
    Senior Member chella182's Avatar
    Joined
    Jan 2008
    Posts
    267

    Covariance and correlation

    I know how to calculate covariance and correlation, just not in this question... I'll explain why after I write out.

    Suppose that X_1, X_2, X_3, X_4, X_5 are independent random variables with variance \sigma^2. Determine the covariance of X_1+3X_2+2X_3 and 2X_1-X_2+3X_4+X_5? Determine the correlation between these two variables.

    Now, as far as I'm aware, you need to know the means to calculate the covariance am I being an idiot and missing something completely obvious?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2008
    From
    Paris, France
    Posts
    1,174
    Quote Originally Posted by chella182 View Post
    I know how to calculate covariance and correlation, just not in this question... I'll explain why after I write out.

    Suppose that X_1, X_2, X_3, X_4, X_5 are independent random variables with variance \sigma^2. Determine the covariance of X_1+3X_2+2X_3 and 2X_1-X_2+3X_4+X_5? Determine the correlation between these two variables.

    Now, as far as I'm aware, you need to know the means to calculate the covariance am I being an idiot and missing something completely obvious?
    You don't need the mean here, simply use the fact that the covariance is bilinear: {\rm Cov}(aX+bY,cZ+dT)=ac{\rm Cov}(X,Z)+ad{\rm Cov}(X,T)+...\mbox{(two terms with $Y$)}, and {\rm Cov}(X,Y)=0 if X,Y are independent, and {\rm Cov}(X,X)={\rm Var}(X).
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member chella182's Avatar
    Joined
    Jan 2008
    Posts
    267
    Quote Originally Posted by Laurent View Post
    You don't need the mean here, simply use the fact that the covariance is bilinear: {\rm Cov}(aX+bY,cZ+dT)=ac{\rm Cov}(X,Z)+ad{\rm Cov}(X,T)+...\mbox{(two terms with $Y$)}, and {\rm Cov}(X,Y)=0 if X,Y are independent, and {\rm Cov}(X,X)={\rm Var}(X).
    Okay, so am I doing 2\times Cov(X_1,X_1)+(-1)\times Cov(X_1,X_2)+3\times Cov(X_1,X_4)+Cov(X_1,X_5)... then with terms starting with 3X_2 and 2X_3 et cetera?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2008
    From
    Paris, France
    Posts
    1,174
    Quote Originally Posted by chella182 View Post
    Okay, so am I doing 2\times Cov(X_1,X_1)+(-1)\times Cov(X_1,X_2)+3\times Cov(X_1,X_4)+Cov(X_1,X_5)... then with terms starting with 3X_2 and 2X_3 et cetera?
    Yes, but since the covariance of independent terms is 0, you can write the terms like {\rm Cov}(X_1,X_1) only, and there are just two of them.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Mar 2009
    Posts
    179
    Thanks
    1
    Is the correlation -1/ \sqrt{210}?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Stats: Covariance and Correlation Matrix
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: September 27th 2011, 04:46 PM
  2. Replies: 1
    Last Post: May 9th 2011, 03:50 AM
  3. Covariance and Correlation
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: May 4th 2009, 07:52 PM
  4. covariance and correlation
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: February 10th 2008, 03:48 AM
  5. probability: covariance and correlation
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: December 3rd 2007, 11:25 PM

Search Tags


/mathhelpforum @mathhelpforum