Exercise 2.11 - Normalization constant for a 1D Gaussian

Answers

We have:

\begin{aligned} C & = \int_{0}^{2 π} \int_{0}^{\infty} r \cdot \exp {- \frac{r^{2}}{2 σ^{2}}} d r d 𝜃 \\ = 2 π σ^{2} \cdot \int_{0}^{\infty} \exp {- u} d u \\ = 2 π σ^{2} . \end{aligned}

For multivariate Gaussian, the trick is to diagonalize the covariance matrix and integrate each component independently.

solour_lfq

2021-03-24 13:42