(a) In a certain economy the marginal propensity to save is 0.2 and the autonomous consumption equals 400. (i) Formulate the consumption function. (3 marks) (ii) If the Government's expenditures were increased by 50% what would be resultant change in National Income. (3 marks)A random variable X has probability density function: f[.r) = L's1x .r z:- a where R is a positive constant and k is a constant. (i) {a} Derive a formula for the moment generating function of X . {b} State the values of r for which your formula in (i](a} is valid. [4] {ii} Hence determine the value of the constant k in terms of R. [1] [Total 5] The random variable U has a geometric distribution with probability function: P(U = 1) = pq"- 1 =1,2,3.... where p+q=1 (i) Derive the probability generating function of U . [2] (ii) Derive the moment generating function of U . [2] (iii) Explain the connection between the PGF and MGF. [1] [Total 5]