Homepage › Solution manuals › Gilbert Strang › Linear Algebra and Learning from Data › Exercise 5.2.1

Exercise 5.2.1

Answers

$p_{1} p_{2} = \frac{1}{2 π σ_{1} σ_{2}} e^{- \frac{x^{2}}{2 σ_{1}^{2}} - \frac{x^{2}}{2 σ_{2}^{2}}} = \frac{1}{2 π σ_{1} σ_{2}} e^{- \frac{x^{2}}{2 \frac{σ_{1}^{2} σ_{2}^{2}}{σ_{1}^{2} + σ_{2}^{2}}}} = \frac{1}{2 π σ_{1} σ_{2}} e^{- \frac{x^{2}}{2 σ^{2}}}$

It’s clear that $σ^{2} = \frac{σ_{1}^{2} σ_{2}^{2}}{σ_{1}^{2} + σ_{2}^{2}}$

Note, the constant in front of the exponential needs to be scaled to make the integration of $p_{1} p_{2}$ equal to 1.

niuers

2020-03-20 00:00

Exercise 5.2.1

Answers

Comments

Add answer