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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 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)