Solve all parts, i'll upvote

A random Gaussian (0, 4) signal X is propagated through a noisy channel. The noise Z is Gaussian (0,3) random variable. (a) Write down the joint PDF of signal and noise. [3 marks] (b ) Y is the signal arrived at a receiver after propagating through a noisy channel with noise Z. Write down the joint PDF between the transmitted and the received signal [3 marks] (c) The first stage of the receiver a linear amplifier with gain a. The output of the amplifier is denoted as Q. Write down the PDF for W when there is no arriving signal. [4 marks]