Question 2 Let X be a random variable with the probability density function fx(x) given by fx(2) = Let Y = 2X - 3. (a) For each of the following statements determine whether it is true or false and briefly justify your answer. The marks will be awarded for the correct justification. (I) Var(Y) = 2 Var(X) [1 mark] (II) corr(X, Y) = 1 [2 marks] (III) cov( X, Y) = 0 [1 mark] (IV) Var(Y - 2X) = 0 [2 marks] (b) Compute the distribution function of X. [3 marks]