Results 1 to 10 of 10
Like Tree4Thanks
  • 1 Post By chiro
  • 1 Post By chiro
  • 1 Post By romsek
  • 1 Post By romsek

Thread: Solving the exponent of e of a bivariate normal density function?

  1. #1
    Junior Member
    Joined
    Nov 2014
    From
    IceLand
    Posts
    28

    Solving the exponent of e of a bivariate normal density function?

    Solving the exponent of e of a bivariate normal density function?-biv222.png


    By the way in the formula above it is

    \frac{1}{2(1-p^2)} not \frac{1}{2(1-p)^2}
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    6,536
    Thanks
    1701

    Re: Solving the exponent of e of a bivariate normal density function?

    Hey littlejon.

    You have to make a comparison between the density function and the parameters.

    What have you tried to answer this question?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Nov 2014
    From
    IceLand
    Posts
    28

    Re: Solving the exponent of e of a bivariate normal density function?

    I tried this so far I am stuck as how to derive  u_1 ,u_2

    Solving the exponent of e of a bivariate normal density function?-mathbi.png

    Their is definitely a connection even when I expanded it I do not see it.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    6,536
    Thanks
    1701

    Re: Solving the exponent of e of a bivariate normal density function?

    It's a lot easier than you might think.

    Take for instance (x+2)^2.

    If you set u1 = -1 and sigma1 = 1 you will get the answer.

    The coefficient outside of the squared term is 1/1 or 1 which gives sigma1 = 1 and inside the squared term you get (x - -2) = (x+2) which means u1 = 1.

    See if you can do the same for the other square term and then later for the correlation coefficient.
    Thanks from littlejon
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Nov 2014
    From
    IceLand
    Posts
    28

    Re: Solving the exponent of e of a bivariate normal density function?

    What aboot  u_2 =-2 That is quite a mystery indeed.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    6,536
    Thanks
    1701

    Re: Solving the exponent of e of a bivariate normal density function?

    You should factor out the sigma term.

    Just remember that 1/x^2 * (a-b)^2 = ([a-b]/x)^2
    Thanks from littlejon
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    5,565
    Thanks
    2348

    Re: Solving the exponent of e of a bivariate normal density function?

    Solving the exponent of e of a bivariate normal density function?-clipboard01.jpg
    Thanks from littlejon
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    6,536
    Thanks
    1701

    Re: Solving the exponent of e of a bivariate normal density function?

    I think you made a mistake with your Mathematica code romsek.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    5,565
    Thanks
    2348

    Re: Solving the exponent of e of a bivariate normal density function?

    Quote Originally Posted by chiro View Post
    I think you made a mistake with your Mathematica code romsek.
    answer seemed to work out pretty nicely. Where do you think the mistake is?

    I ignored the $(x-\mu_1)$ and $(y-\mu_2)$ terms since they so clearly match up with what's given.

    all that's left to be solved for is $\sigma_1, \sigma_2, \rho$
    Thanks from littlejon
    Follow Math Help Forum on Facebook and Google+

  10. #10
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    6,536
    Thanks
    1701

    Re: Solving the exponent of e of a bivariate normal density function?

    I concede I made a mistake - sorry about that.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: Dec 5th 2012, 04:40 PM
  2. Normal / Bivariate Normal distribution
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: May 24th 2010, 03:42 AM
  3. bivariate normal function
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: Feb 7th 2010, 02:06 PM
  4. How do I proof standard normal density function
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: Mar 27th 2009, 08:20 AM
  5. bivariate marginal density function
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: Apr 8th 2008, 05:23 AM

Search Tags


/mathhelpforum @mathhelpforum