b) Let S be a continuous random variable representing the students' study time (in hours) for their Statistics final paper. The probability density function is given by: 45 f(s) : (2+ 15' 1ss54 , otherwise i) Calculate the expected value of S. (4 marks) ii) Calculate the variance of S. (6 marks) iii) Determine E (1145 - 7S - 6S?). (2 marks)