Gaussians Pieter Abbeel UC Berkeley EECS Many slides adapted from Thrun , Burgard and Fox, Probabilistic Robotics. TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A A A A A A A A A A A A A. Outline. Univariate Gaussian Multivariate Gaussian
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UC Berkeley EECS
Many slides adapted from Thrun, Burgard and Fox, Probabilistic Robotics
TexPoint fonts used in EMF.
Read the TexPoint manual before you delete this box.: AAAAAAAAAAAAA
Disclaimer: lots of linear algebra in next few lectures. See course homepage for pointers for brushing up your linear algebra.
In fact, pretty much all computations with Gaussians will be reduced to linear algebra!
(integral of vector = vector of integrals of each entry)
(integral of matrix = matrix of integrals of each entry)
Multi-variate Gaussians: examples
We integrate out over y to find the marginal:
Hence we have:
Note: if we had known beforehand that p(x) would be a Gaussian distribution, then we could have found the result more quickly. We would have just needed to find and , which we had available through
Hence we have: