Good morning every body
Please help me as soon as possible and thanks’ a lot

1-9: hypothesis testing with correlated noise: consider the hypothesis

H0 = 0 and H1 different of 0
And the observations: zi= θ + wi i = 1,…,n
With wi zero-mean jointly Gaussian but not independent. Denoting
w = [ w1 … wn]’
One has the covariance matrix (assumed given) E[w*w’] = P

For the above:
1- Specify the optimal hypothesis test for false alarm probability α
2- Solve explicitly for n=2, P = [1 05; 0.5 1] and α = 1%.


1-10: Partial derivative with respect to a matrix:
the partial derivative of a scalar q with respect to the matrix A = [aij] is defined as [∂q/∂A] = [∂q/∂aij]

Prove that:
1- For B symmetric , [∂tr[ABA’]/∂A] = 2AB
2- For B not symmetric, , [∂tr[AB]/∂A] = B’