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Let's think we have a multivariate normal distribution with $$\mathbf x_1=\begin{bmatrix}x_{11}\\x_{12}\end{bmatrix},\quad \mathbf x_2=\begin{bmatrix}x_{21}\\x_{22}\end{bmatrix},\quad\mathbf m=\begin{bmatrix}m_1\\m_2\end{bmatrix}, \quad\text{and}\quad\mathbf S.$$ Where $\mathbf m$ is the mean, and $\mathbf S$ is a $2\times 2$ covariance matrix.
The PDF $p$ of a, say, bivariate Normal distribution with mean $\mu$ and covariance $S$ is a function that takes two parameters and has a scalar-valued output:
$$ p: \mathbb{R}^2 \mapsto \mathbb{R}$$
and is given by
$$p(x_1,x_2) = \frac{1}{2\pi |S|}\exp\left(-\frac{1}{2}(\vec{x}-\vec{\mu})^TS^{-1}(\vec{x}-\vec{\mu})\right)$$
where $\vec{\mu}\in\mathbb{R}^2$ is the mean of the distribution and $S\in\mathbb{R}^{2\times 2}$ is its covariance matrix. $\vec{x}=[x_1, x_2]^T$ is the function input and $p(x_1, x_2)$ is the function output.
So, the output is a scalar (a single value). Furthermore, the PDF can become larger than one for some input $\vec{x}$.
