Determine a gaussian rve with mean vector-covariance matrix

Question

Assignment:

1. Let x a Gaussian rve with mean vector and covariance matrix

m_x = [2 _-1] , k_x = [1 0 _{0 3}]

and let z = x₁ + x₂. Are x₁ and x₂ statistically independent? Write the expression of pz(a).

2. Consider the rve x = [x₁, x₂] having PDF

a) State whether x₁, x₂ are statistically independent and give the expression of the conditional PDF px₁|x₂ (a₁|a₂).

b) Find the value of c for λ = 1.

c) Does a linear invertible transformation y = Ax exist such that y is a Gaussian rve?