2d normal distribution equation?

[Cheetah Designs]

Is this correct:

f(x, y) = (1 / ( sqrt(2 * Pi) * sigma_x * sigma_y )  ) * exp ( - ( (x-mu_x)^2 / 2sigma_x^2 ) + ( (y-mu_y)^2 / 2sigma_y^2 ) )

 

[RomanNose]

Lol wut?

 

[muon]

Is this correct:

f(x, y) = (1 / ( sqrt(2 * Pi) * sigma_x * sigma_y )  ) * exp ( - ( (x-mu_x)^2 / 2sigma_x^2 ) + ( (y-mu_y)^2 / 2sigma_y^2 ) )

Trying to read that makes my head hurt.

Here's the answer.

http://en.wikipedia.org/wiki/Multivariate_normal_distribution#Bivariate_case

 

[Craig1981]

......Yes?

 

[SuperTronNarwhal]

No Why? You forgot to Add (- ( Plus here ( x-MU_x)

 

[muon]

No Why? You forgot to Add (- ( Plus here ( x-MU_x)

Ignored the covariance most crucially.

edit:

you don't need the "+" there, it makes no difference?

 

[D.P.]

Is this correct:

f(x, y) = (1 / ( sqrt(2 * Pi) * sigma_x * sigma_y )  ) * exp ( - ( (x-mu_x)^2 / 2sigma_x^2 ) + ( (y-mu_y)^2 / 2sigma_y^2 ) )

http://upload.wikimedia.org/wikipedia/en/math/1/9/8/1983171154842b0b061fc42aa5eb7642.png
http://en.wikipedia.org/wiki/Multivariate_normal_distribution#Bivariate_case

 

[Reaper 392]

could you put your equation in here and see what it looks like please
http://www.forkosh.com/mimetextutorial.html

then i might be able to decipher it

 

[Tefal]

Ignored the covariance most crucially.

More worryingly he forgot to invert the tachyon beam!

 

[muon]

http://upload.wikimedia.org/wikipedia/en/math/1/9/8/1983171154842b0b061fc42aa5eb7642.png

But isn't that under a certain covariance matrix?

So it isn't the general form.

edit:

Either way, I feel sorry for the people having to do statistics. It is so dull and difficult to remember. Okay, maybe not to Maths students.

 

[D.P.]

But isn't that under a certain covariance matrix?

So it isn't the general form.

edit:

Either way, I feel sorry for the people having to do statistics. It is so dull and difficult to remember. Okay, maybe not to Maths students.

Yes, I edited to give the more general case.

Wh is to say this is stats. I use multi-dimensional gaussians hell of a lot in many different problems, often in machine learning. True that they may be related to statistical techniques, but then computer science is just a form of mathematics.

 

[Reaper 392]

ok, i was curious (and very bored) so i tried to decipher what you wrote in that program myself.

as far as i can see, this is what you've written: