Consider a probabilistic model that has a numerical parameter . A "probabilistic model" is just a set of assumptions about randomness. Let the random variable be an estimator of . Frequently, is a statistic based on a random sample. The bias of is defined as where the subscript reminds us that is the true value of the parameter. Note that is a real-valued function of , not a random variable. Recall that is an unbiased estimator of if , that is, if . But in general, estimators are biased. The mean squared error of the estimator is Follow the calculation in Section 12.2 of the textbook to show the bias-variance decomposition given by Note that the square in the bias term makes sense. Bias has the same units as , whereas the MSE and variance are in the square of those units