= Solution
{c}
The joint <maximum-likelihood estimators> are functions of the observations selecting a maximizing parameter pair:
$$
\boxed{(\widehat\mu,\widehat\lambda)\in
\operatorname*{arg\,max}_{\mu\in\mathbb R,\lambda>0}
L(\mu,\lambda;X_1,\ldots,X_n).}
$$
The <estimates> after observation maximize the same <likelihood function> with $X_i=x_i$. Maximization may be nonunique, as for an even <sample size>, or may fail to yield a finite admissible pair, as in the one-observation case below. The definition does not turn a boundary supremum into an attained <maximum>.
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