Mutual Information from this Gaussian Distribution

Arman777
Insights Author
Gold Member
Messages
2,163
Reaction score
191
Homework Statement
Calculating Mutual Information from Gaussian
Relevant Equations
Statistics Equations
Let us suppose we are given a Gaussian Distribution in the form of

$$p(x,y) \propto exp(-\frac{1}{2}x^2 - \frac{1}{2}by^2 - cxy)$$ What are the equations that I need to use to obtain Mutual Information ?
 
Physics news on Phys.org

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
View full post »

Similar threads

Understanding the meaning of "expected fraction" (Statistics)
Replies
4
Views
2K
Total movement of bacteria assuming a random distribution
Replies
5
Views
1K
Determine marginal densities and distributions from joint density
Replies
7
Views
1K
Problems with Gaussian distribution
Replies
2
Views
2K
Consider the Gaussian Distribution....?
Replies
4
Views
2K
Linear combination of random variables
Replies
18
Views
2K
Understanding Conditional Expectation, Variance, and Precision Matrices
Replies
0
Views
751
Calculating a moment of a distribution
Replies
11
Views
2K
Integrating Gaussian Distribution (QM)
Replies
10
Views
2K
Showing a Distribution is Gaussian
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top