V(X) is the variance (Variance - Wikipedia)
E[X] is the expected value (Expected value - Wikipedia)
X is the probability law which gives the probability of a pixel to have a particular brightness value.
You can compute E[X] and V(X) by taking a defocused shot I_n of a linear gradient (https://drive.google.com/file/d/1e6_a0Rs8sBcEZR1jnlUbFyYWB2zNKbfR/view?usp=drivesdk), and then compute a mean filter (or gaussian blur if you prefer) on this image to get a reference image I_r of what the image would be without noise.
Then, the expected value E[X] at each pixel is approximated by the pixel value on I_r.
The variance is computed by gathering all the pixels that have the same value in I_r, and computing the average of (I_n[pixel]-E[X])^2.
I used shots like these to create the graphs: https://drive.google.com/open?id=1YZS7PmqSIQFdJn0KzHdXiiW3U_tYkdHZ
These shots are 2 shots of a BW linear gradient (you can find it here: https://drive.google.com/open?id=1e6_a0Rs8sBcEZR1jnlUbFyYWB2zNKbfR), at +3EV and -3EV, to capture all the dynamic range of the camera.