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’