# Find the ML estimate of lambda for $X=(X_1,\ldots,X_n)$, $X_i$ iid with pdf $g = \lambda y^{-2}, y>\lambda$, $\lambda>0$ [duplicate]

Let $$X=(X_1,\ldots,X_n)$$, with $$X_1,\ldots,X_n$$ iid and $$X_i$$ with cts distribution having pdf,

\begin{align} g_\lambda (y) &= \begin{cases} \lambda y^{-2}, & y \geq \lambda\\ 0, & \text{else} \end{cases} \end{align} where $$\lambda >0$$

We are asked to find the ML estimate of $$\lambda$$

I have \begin{align} L &= \prod_{i=1}^n g_\lambda (x_i) = \lambda^n \prod_{i=1}^n x_i^{-2} \end{align} for the likelihood function but I'm stuck on how to find the MLE.

All I've really noticed is that $$L \neq 0$$ when $$\min\{x_i,\ldots,x_n\}\geq \lambda$$ and my first attempt says that the MLE for $$\lambda$$ is infinite.