Control variates: Difference between revisions

:<math>I \approx \frac{1}{n} \sum_i f(u_i); </math>
 
Now we introduce <math>g(x) = 1+x</math> as a control variate with a known expected value <math>\mathbb{E}\left[g\left(U\right)\right]=\int_0^1 (1+x) \, \mathrm{d}x=\frac{3}{2} </math> and combine the two into a new estimate
:<math>I \approx \frac{1}{n} \sum_i f(u_i)+c\left(\frac{1}{n}\sum_i g(u_i) -3/2\right). </math>
 
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