Not sure if my question is a valid one but I will just put it out here.
Consider a bivariate data set $(x_i, y_i)$ $[i=1,...,n]$ to which a bivariate Gaussian Distribution is fitted. Now, consider a data point $z=(x_p, y_p)$. I wish to express the Euclidean distance of $z$ from the bivariate Gaussian mean $(\mu_1, \mu_2)$ in terms of $\sigma$, the variance-covariance matrix here. Can this be done?
My motivation for this question comes from the univariate case wherein the aforementioned distance can be obtained easily. Can this be done for the bivariate case? If yes, any assistance in terms of theory or R code would be helpful as I am clueless about both. Thanks!