1. Let x a Gaussian rve with mean vector and covariance matrix and let z = x 1 + x 2 . Are x 1 and…
1. Let x a Gaussian rve with mean vector and covariance matrix
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?
