3. A receiver in a multiuser communication system accepts K binary signals from K independent transmitters: $Y = (Y_1, Y_2, \dots, Y_K)$, where $Y_k$ is the received signal from the $k^{th}$ transmitter. In an ideal system the received vector is given by:
$Y = Ab + N$
where $A = [a_k]$ is a diagonal matrix of positive channel gains, $b = (b_1, b_2, \dots, b_K)$ is the vector of bits from each of the transmitters where $b_k = \pm 1$, and N is a vector of K independent zero-mean, unit-variance Gaussian random variables.
Find the joint pdf of Y.
Suppose $b = (1, 1, \dots, 1)$, find the probability that all components of Y are positive.
