Based on the discussions in Photon counting noise and Instrumental noise, depending on the values you specify for \(B\) and \(C\) from the above, the final noised value for each pixel is a random value chosen from a Gaussian distribution with
$$\mu=B+I_{nn}, \quad \sigma=\sqrt{C^2+B+I_{nn}}$$
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GNU Astronomy Utilities 0.23 manual, July 2024.