how to calculate the MLEs of the 5 parameters of a bivariate normal population, the parameters being ?

while trying to solve for , i got the following equation

is this correct? how can i solve for from here?

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- Nov 26th 2010, 10:16 PMSambitMLE of bivariate normal
how to calculate the MLEs of the 5 parameters of a bivariate normal population, the parameters being ?

while trying to solve for , i got the following equation

is this correct? how can i solve for from here? - Nov 26th 2010, 10:55 PMmatheagle
you need to take the partial derivative wrt to all 5 parameters

It's smart to take the logarithm of the joint density first - Nov 27th 2010, 04:14 AMSambit
I took the logarithm and differentiate partially wrt and got that

- Nov 27th 2010, 07:11 AMmatheagle
you need to solve all five together, the MLE of should be

and those for the population variances should be the sample variances with n in the denomiator.