In an acquisition of computers for 100 employees of a company, one computer each employee. The computers are expected to serve for three years before they are retired and donated to a local school. Each computer costs $1,000 to acquire now.

Suppose each computer fails each year independently with probability 3%. That is, each computer fails with the same probability (3%) in year 1, in year 2, and in year 3.Once a computer fails it needs to be replaced right away. If a computer fails in the first year, the vendor will replace it at no charge. Suppose for now an identical computer is purchased as replacement if a computer fails in Year 2 or Year 3. Due to innovation and technological advances, the price is discounted by a factor of 0.9 each year, meaning the same computer costs 0.9*$1,000 (in today's money) to replace anytime in the second year, and only 0.9*0.9*$1,000 (in today's money) to replace anytime in the third year. From now on, all dollar amounts are in today's money.

Q) Think of the total replacement cost spent on a typical employee. It is 0 if the employees computer never fails, it may be replaced in Year 2 at $900, and it may also be replaced in Year 3 at $810. If you use a random variable to describe it, what are all the possible values and what is the probability mass function of this random variable? What is the expectation of the total replacement cost (in today's money) for all 100 computers in the next three years? If you just budget the amount you obtained in the preceding question, there is a good chance you will run into deficit. On the other hand, if you budget $500 per employee, you are likely to use only a small portion of it. Suppose you wish to budget for the least amount that is needed so that with probability 97.5% you have just enough. How much do you need to budget for?