Which of the following mean is a mixture of the MLE and the prior mean?

The correct answer is C. posterior.

The posterior mean is a weighted average of the prior mean and the MLE, where the weights are determined by the likelihood function. The posterior mean is a more informative estimate of the parameter than either the prior mean or the MLE alone, because it takes into account both the prior information and the data.

The interior mean is the mean of the data, while the exterior mean is the mean of the prior distribution. Neither of these means is a mixture of the MLE and the prior mean.