Question 2: Suppose two random variables 1: and z are related by the following equation: 2 z=zz+2z+%e, where e is a random variable that follows the normal distribution N(0, 1), i.e., 1 --' = T. 10(6) me What is the density function of the conditional distribution p(z|:r)? (Note that the purpose of this problem is to help you understand reparameterization.) Solution: Since 6 is Gaussian, z is also Gaussian. Its means is ,u, = 1'2 + 22:, and its variance is 0'2 = 22/2. Hence, its density function is: p(2|1) =