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I was referring to this lecture Markov Chain Monte Carlo. However, I didn't get how the $\pi$ value was calculated. Here is a screenshot

enter image description here

As far as I know the integral gives the area under the curve. So I didn't get how the double integral is giving the value of $\pi$ using $P(x,y)$.

Also how did it convert to mean in Octave. I am just a beginner. So please some guidance is required

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