4 A random variable Y has probability density function f(y) = ae - Sy, y>b, where a, b are positive constants. The moment generating function of Y is denoted by My(t). (i) Write down the bounds of the integration required to calculate My(t). [1] (ii) Identify which one of the following options gives the correct expression for My(t). [2] A1 e-(1-5) a 1-51 -(1-50) a A2 b 1-51 A3 -(S-16 ae b 5-1 e-(5-1) A4 a 5-1 (iii) Write down the condition on t for My(t) to be finite. [1] (iv) Determine an expression giving the constant a in terms of b, using your answer for My(t) from part (ii). [3] [Total 7] 4 A random variable Y has probability density function f(y) = ae - Sy, y>b, where a, b are positive constants. The moment generating function of Y is denoted by My(t). (i) Write down the bounds of the integration required to calculate My(t). [1] (ii) Identify which one of the following options gives the correct expression for My(t). [2] A1 e-(1-5) a 1-51 -(1-50) a A2 b 1-51 A3 -(S-16 ae b 5-1 e-(5-1) A4 a 5-1 (iii) Write down the condition on t for My(t) to be finite. [1] (iv) Determine an expression giving the constant a in terms of b, using your answer for My(t) from part (ii). [3] [Total 7]