# Finding the probablity density of a point for a multivariate gaussian distribution

I just learnt this and it's formula but don't know how to use it.

The question i've been given is:

"What is the density probability of a point at x=[1,2] for a multivariate Gaussian distribution with mean mu=[0.75,2.5] and covariance matrix V=[[4.0, 2.5], [2.5, 6.0]]?"

I have no idea how to approach it. Can anyone show me how to calculate it?

Much appreciated.

The equation i have is:

$$$$f(x,y) = \frac{1}{2 \pi \sigma_x \sigma_y \sqrt{1-\rho^2}} \exp\left( -\frac{1}{2(1-\rho^2)}\left[ \frac{(x-\mu_x)^2}{\sigma_x^2} + \frac{(y-\mu_y)^2}{\sigma_y^2} - \frac{2\rho(x-\mu_x)(y-\mu_y)}{\sigma_x \sigma_y} \right] \right)$$$$