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Maximum likelihood estimator for a discontinuous PDF

Cross Validated Asked by probdiscr on August 17, 2020

Suppose I have a PDF with the following distribution: $theta$ between $[-1, 0]$ and $(1-theta)$ between $[0,1]$.

How can I calculate the MLE estimator for $theta$ in this setting? My first approach would be to treat this distribution as if it were a Bernoulli, but it is not quite right, so I am insecure about that.

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