Lecture 12: Monte Carlo Integration (39)

p1p_1 here gives a result that has a lower variance. For p2p_2, if the random sampling hits the left side of the graph with the smaller probability, it has a huge impact on the estimation, thus introducing variance.


f(x)/p1(x) gives a closer value to 1 throughout the entire graph. However, f(x)/p2(x) is much higher than 1 on the left side while much lower than 1 on the right side. This should give some intuition as to why f(x)/p2(x) has higher variance due to a wider distribution.

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