Priors and Peaks

You fit a Gaussian generative classifier (Gaussian discriminant analysis) on a labeled training set with $K$ classes. Using maximum likelihood, what are the standard estimates for the class prior $\pi_k$ and the class mean $\mu_k$ ?

$\pi_k$ is the sample mean of class $k$ , and $\mu_k$ is the fraction of training examples in class $k$

$\pi_k$ is the fraction of training examples in class $k$ , and $\mu_k$ is the sample mean of the feature vectors belonging to class $k$

$\pi_k$ is always set to $1/K$ regardless of class sizes, and $\mu_k$ is the mean of the entire training set

$\pi_k$ and $\mu_k$ are both found by running logistic regression separately for each class