Consider the random variables X and Y, where X ~ U(1, 2) and Y|X = x ~ N(x, x²). (a) Write down E(Y|X = x) and use the method of iterated expectation to find E(Y). [3 marks] (b) Write down Var(Y|X = x) and use the method of iterated variance to find the variance of Y. [5 marks] (c) Find the joint probability density function, fx,y (x, y), of X and Y
