I know this expression should return a Gaussian distribution but I can't get Mathematica to simplify the integral. What am I missing?(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\text{Simplify}\left[\frac{\text{Product}\left[\text{PDF}\left[\text{NormalDistribution}[y,\sigma ],x_i\right],\{i,n\}\right]\text{PDF}[\text{NormalDistribution}[\mu ,\phi ],y]}{\text{Integrate}\left[\text{Product}\left[\text{PDF}\left[\text{NormalDistribution}[y,\sigma ],x_i\right],\{i,n\}\right]\text{PDF}[\text{NormalDistribution}[\mu ,\phi ],y],\{y,-\text{Infinity},\text{Infinity}\},\text{Assumptions}\to \{\sigma >0,\phi >0\}\right]},\{\sigma >0,\phi >0\}\right]

[/tex]

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# Simplify this expression with Mathematica

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