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where <math>\xrightarrow{\mathcal{D}}</math> denotes convergence in ''distribution'' and <math>Y_x</math> has a normal distribution with mean <math>0</math> and variance <math>\sigma^2(x)</math>, written as <math>\mathcal{N}(0,\sigma^2(
In other words, <math>\hat{g}_N(x)</math> has ''asymptotically normal'' distribution, i.e., for large <math>N</math>, <math>\hat{g}_N(x)</math> has approximately normal distribution with mean <math>g(x)</math> and variance <math>\frac{1}{N}\sigma^2(x)</math>. This leads to the following (approximate) <math>100(1-\alpha)</math>% confidence interval for <math>f(x)</math>:
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