as a part of a theoretical homework I should draw a graphical model for bayesian inference of a mixture of gaussians. Besides this I should make sure that the model is in the exponential family such that Gibbs sampling and Variational Bayesian inference can be applied.

What does this mean? Can someone pls explain to me in an easy way what's the theoretical background behind this question?

Additionally I should identify the conjugate exponential family distributions for univariate and multivariate gaussians.

How should I start solving this question?