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The maximum likelihood estimator (MLE) is the value of the parameter that maximizes the likelihood function for the observed data. Graphically, it is the parameter value at the peak of the likelihood curve.

Conditions: A likelihood function $L(\theta \mid x_1, \dots, x_n)$ has been constructed.; One compares values of the parameter with the data fixed.

The maximum likelihood estimator (MLE) is the value of the parameter that maximizes the likelihood function for the observed data. Graphically, it is the parameter value at the peak of the likelihood curve.

Conditions: A likelihood function $L(\theta \mid x_1, \dots, x_n)$ has been constructed.; One compares values of the parameter with the data fixed.