1. Math
  2. Advanced Math
  3. let two variables x1 and x2 are bivariately normally distributed...

Question: let two variables x1 and x2 are bivariately normally distributed...

Question details

Let two variables X, and X2 are bivariately normally distributed with mean vector components μ1 and μ2 and co-variance matrix Σ shown below: (a) What is the probability distribution function of joint Gaussian P(X1,X2)? (show it with μ and Σ) [5pts] (b) What is the eigenvalues of co-variance matrix Σ? [10pts] (c) Given the condition that the sum of squared values of each eigenvector are equal to 1, what is the eigenvectors of co-variance matrix xf + x-1 ) [10pts] ? (For example, if an eigenvector is vi- ,then T2

Let two variables X1 and X2 are bivariately normally distributed with mean vector components µ1 and µ2 and co-variance matrix Σ shown below:

(a) What is the probability distribution function of joint Gaussian P(X1, X2)? (show it with µ and Σ)

(b) What is the eigenvalues of co-variance matrix Σ?

(c) Given the condition that the sum of squared values of each eigenvector are equal to 1, what is the eigenvectors of co-variance matrix Σ? (For example, if an eigenvector is v1 = [x1 x2] , then x^2_1 + x^2_2 = 1)

Solution by an expert tutor
Blurred Solution
This question has been solved
Subscribe to see this solution