Maximum Likelihood Estimation of Parameters for Random Variables

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Concepts in probability and statistics can be somewhat elusive due to the combination of high level mathematics, bad notation, and entanglement of random variables and data. This article sheds light on the relationship between random variables and data in the context of estimators, estimates, bias and variance, and the method of maximum likelihood estimation.

The article will be broken up into the following sections.

- Parameters of Probability Mass and Distribution Functions

- Estimators

- Estimates

- Bias and Variance

- Maximum Likelihood Estimation