# How to deal with mixture of continuous and discrete features when using Naive Bayes classifier

My task is to use Naive Bayes classifier for prediction, where I have both continuous and discrete variables as predictor variables. In literature the classifier is written as:

$$\hat{y}= \underset{k\;\in\;\{1,..K\}} {\mathrm{argmax}} \;\;P(C_k)\prod_{i=1}^np\left(x_i\;|\;C_k\right),$$

where $P$ is a probability and $p$ is a probability density function. What if some of my features $x_i$ are discrete variables and some are continuous? Does the decision rule just become into:

$$\hat{y}= \underset{k\;\in\;\{1,..K\}} {\mathrm{argmax}} \;\;P(C_k)\prod_{i=1}^mp\left(x_i\;|\;C_k\right)\prod_{j=m}^nP\left(x_j\;|\;C_k\right)\;\;?$$