def _get_mean_and_sigma_of_product_of_two_gaussians(mean1, mean2, var1, var2):
    """
    product of two gaussian pdfs is a gaussian with mean = (var1 * mean2 + var2 * mean1) / (var1 + var2) and var = (1/var1 + 1/var2)^ -1
    """
    return (mean2 * var1 + mean1 * var2) / (var1 + var2), ((1 / var1) + (1 / var2)) ** -1