Let X,Y and Z be jointly continuous random variables. Consider the random vector W = [X X U[1,2], Y where Y|X = x Exp(1/x), Z] Z|X = x,Y = y N(x,1).

Let X,Y and Z be jointly continuous random variables. Consider the random vector

W = [X                      X ∼ U[1,2],

         Y        where   Y|X = x ∼ Exp(1/x),

         Z]                     Z|X = x,Y = y ∼ N(x,1).

Find the mean vector and covariance matrix of W.