The owner of'a small restaurant has found daily net revenue has a mean of $1,112 and standard deviation of $2,134. The restaurant is open 300 days per year and the annual xed costs are $300,000. (a) (b) (C) Assuming each operating day's net revenue is independent from all the others, find the probability that the restaurant will cover its xed costs over a year. [2 marks] Now, assume net revenues from operating day i and operating day j have correlation 0.5'i'j'. Find the probability the restaurant will cover its xed costs over a year. [NOTE: It j I simply represents the number of operating days between the revenues. Further, in a collection of 300 consecutive operating days, 299 pairs are one day apart, 298 pairs are two days apart and so on. Finally, recall that for any random variable X, we know Var(X) = Cov(X , X) and remember how useful Excel can be for calculations] [1 mark] The restaurant has dine-in and take-away. Daily net revenues om each are normal with mean $556 and standard deviation $2,134, and they are anti-correlated with p = O.5. On the last operating day of the year, total net revenue to date is $299,093. The dine-in operation (which closes earlier than take-away) had net revenue of $452. Given this, what is the chance today's take-away net revenue will allow the restaurant to cover its annual xed costs? [2 marks]