= Solution
{c}
Let $M=\max_iX_i$. For an observed sample in the nonnegative orthant, the <likelihood function> under the <uniform distribution> is
$$
L(\theta)=\theta^{-n}\mathbf1_{\{\theta\ge M\}},\qquad\theta>0.
$$
It is zero for $\theta<M$, and decreases with $\theta$ on $[M,\infty)$. Thus the <maximum likelihood estimation> problem is solved at the smallest admissible value:
$$
\boxed{\widehat\theta=M=\max_{1\le i\le n}X_i.}
$$
Under the model $M>0$ with <probability> one. The all-zero sample is a null event on which the <likelihood function> has no finite maximizer in the parameter space $\theta>0$.
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