def gaussian_pdf(x: str = 'x', mean: str = r'\mu', variance: str = r'\sigma^2') -> str:
    """
    Returns a string representing the probability density function for a Gaussian distribution.

    **Parameters**

    - `x`: str

        The random variable.

    - `mean`: str, optional

        The mean of the random variable.

    - `variance`: str, optional

        The variance of the random variable.

    **Returns**

    - `out`: str

        TeX compatible string.
    """

    return r'\frac{1}{\sqrt{2\pi ' + variance + r'}}e^{-\frac{(' + x + '-' + mean + r')^2}{2' + variance + r'}}'