Solution
= Solution
Put $M_n=\max_{1\leq i\leq n}|X_i|$. The likelihood is
$$
L(\theta)=\frac1{(2\theta)^n}\mathbf1_{\{\theta\geq M_n\}}.
$$
It decreases on its nonzero range, so
$$
\boxed{\widehat\theta=M_n.}
$$
= Solution
Put $M_n=\max_{1\leq i\leq n}|X_i|$. The likelihood is
$$
L(\theta)=\frac1{(2\theta)^n}\mathbf1_{\{\theta\geq M_n\}}.
$$
It decreases on its nonzero range, so
$$
\boxed{\widehat\theta=M_n.}
$$