- #1
dabd
- 25
- 0
I know this expression should return a Gaussian distribution but I can't get Mathematica to simplify the integral. What am I missing?
[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]
[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]