Question: Ali would like to make some money as a part-time travelling salesman. Unfortunately he has some debts overdue, so the sum of money coming from his first sale is sure to pay off some of his debts; Ali is going to begin enjoying his income from the second sale on. He has got only Sundays to spare for such a job, and this is a Sunday, the first attempt on convincing people to buy his stuff is to take place next week on Sunday. Sale attempts independently take place one at a time weekly, and Ali’s probability of concluding an attempt successfully is p. The money he makes at a single successful attempt, independent of any other try, is uniformly distributed between a L and a H. Ali has a head for business and is aware of inflation, which devaluates the currency at an exponential rate of rw per week. Ali sits down today (remember this is a Sunday, a week before his first attempt) and would like to compute the following items parametrically, about the current value of his possible earnings in today’s terms of money. Would you like to help him with his calculations?

a- What is the expected sum Ali may make on his 2nd and 3rd successful attempts together at sales, in today’s money?

b- If Ali’s earnings from his 2nd sale happens to be more than M dollars in today’s money, then what is the probability that the first successful sale attempt comes after the week with index j, with 1 as the index of the first attempt to take place next Sunday?