Why does maximum likelihood estimation for uniform distribution give maximum of data? I am looking at parameters estimation for the uniform distribution in the context of MLEs.  Now, I know the likelihood function of the Uniform distribution $U(0,\theta)$ which is $1/\theta^n$ cannot be differentiated at $\theta$. The conclusion is that the estimate of $\theta$ is $\max(x_i)$, where $x_1,x_2,\ldots,x_n$ is the random sample. I would like a layman's explanation for this.

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