Consider estimating the parameters of a multivariate

Question

Problem

a. Consider the task of estimating the parameters of a univariate Gaussian distribution N µ; σ²  from a data set D. Show that if we maximize likelihood subject to the constraint σ² ≥ ? for some ? > 0, then the likelihood L(µ, σ² : D) is guaranteed to remain bounded.

b. Now, consider estimating the parameters of a multivariate Gaussian N (µ; Σ) from a data set D. Provide constraints on Σ that achieve the same guarantee.