Likelihood of bivariate Gaussian distribution

Let X, one observation composed of two values (x1, x2) obtained from Gaussian distributions µ1, s1 and µ2, s2 with rho being a correlation coefficient between Gaussian distributions 1 and 2, the likelihood is:

library(mvtnorm)

dmvnorm(x=c(x1,x2), mean=c(µ1,µ2), sigma=matrix(c(s1, rho, rho, s2), ncol=2))

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