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

1. ## Solving the exponent of e of a bivariate normal density function?

By the way in the formula above it is

$\displaystyle \frac{1}{2(1-p^2)}$ not $\displaystyle \frac{1}{2(1-p)^2}$

2. ## 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?

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

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

Their is definitely a connection even when I expanded it I do not see it.

4. ## 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.

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

What aboot $\displaystyle u_2 =-2$ That is quite a mystery indeed.

6. ## 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

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

Originally Posted by chiro
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 $\sigma_1, \sigma_2, \rho$