I have a question about MLE and how it relates to OLS. I know how to relate OLS and MLE when the noise is normal and homoskedastic. I can apply the same reason for heteroskedastic noise. My question is that, clearly, the noise terms are no longer identical (though still independent). So, we can apply MLE even when the distributions are not identical?

To make it more clear, if I take two samples, can I apply MLE when one sample's noise is normal, and the other's is laplace? If not, why does MLE work for heteroskedastic noise?

Is it because, when estimating the parameter vector, we can simply take the different variances as known scaling factors* uniform variance $\sigma^2$, giving rise to the weights?