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\begin{equation}
  P(x)=\cos^2\theta \frac{1}{\sqrt{2\pi\sigma_1^2}}e^{-\frac{x^2}{2\sigma_1^2}}+\sin^2\theta \frac{1}{\sqrt{2\pi\sigma_2^2}}e^{-\frac{x^2}{2\sigma_2^2}}
\end{equation}
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