QUESTION 1 (12 marks) A farmer must get a fox, a goose, and a bag of corn across a river in a boat which is only large enough for her and one of these three items. She does not want to leave the fox alone with the goose nor the goose alone with the corn. How can she get all these items across the river?
Construct a flowchart to describe how the farmer can get herself, the fox, the goose, and the bag of corn across the river.

In any one-minute interval, the number of requests for a popular web page is a poisson random variable with expected value 240 requests. (a) a web server has a capacity of requests per minute. if the number of requests in a one-minute interval is greater than the server is overloaded. use the central limit theorem to estimate the smallest value of for which the probability of overload is less than 0.035. note that your answer must be an integer. also, since this is a discrete random variable, don't forget to use "continuity correction". = 268 (b) now assume that the server's capacity in any one-second interval is ⌊/60⌋, where ⌊⌋ is the largest integer ≤ (this is called the floor function.) for the value of derived in part (a), what is the probability of overload in a one-second interval? this time, don't approximate via the clt, but compute the probability exactly.