Let the random variable X be the demand for newspapers at a news stand. X is Discrete Uniform distributed from 10 to 20

f(x) =1/11 for x{10,11,....,20}

At the start of the day the newsboy buys papers for 25 cents apiece. Hesells papers for 75 centsapiece. If there are any papers left over at the end of the day, he maysell the papers to the recycling company for 5 cents apiece. How many papers should the newsboy buy at the start of the day to maximize expected profit? (Note: this is a very famous problem in inventory theory called "The Newsboy Problem". It captures the essential inventory problem faced by many companies, namely how much product should we have in the face of random demand?)

1. Suppose the newsboy decides to buy 15 papers (the expected demand). What will his profit be? Hint: use the table below, then calculate E(Total Revenue), then E(Profit). Use Excel for calculations.