I want some help for this q

2. Bob is taking two exams shortly1 one on statistics and the other on accounting. He plans to allocate a proportion to of his revision time for statistics and the remaining 1 w for accounting, for some to 6 [0,1]. Let Bob's exam scores for statistics and accounting be given by 100 53 "' and 100 e\"; '1'\"), respectively1 where S and A are independent positive random vari- ables. (a) The moment generating functions of S and A are given respectively by 5 20 Mt=lt Mt=lt2. 3U 5_t{ 0} and FAQ?) = (1 8\") H: > 0}. In the exam of any subject, a score lower than 40 is regarded as a failure. Bob will be discontinued if he fails his exams for both statistics and accounting. Determine the optimal value ml of the proportion in which minimises Bob's probability of discontinuation. [6 marks]