Tourists wait at the Oamaru water front at dusk for the little blue penguins to return from a day in the ocean. Assume that penguin arrivals follow a Poisson process with parameter /\\ = 10 penguins per hour. (a) How long does a tourist who is watching the penguins has to wait on average until a new penguin arrives? @ (b) What is the expected number of penguins that arrive while a tourist watches for penguins for 20 minutes? a (c) When a new tourist arrives at the water front, she is told that no penguin came to shore for the last 10 minutes What is the probability that she has to wait at least another 10 minutes until a penguin arrives? ' (d) What is the probability that exactly 2 penguins arrive between 7:20pm and 7:30pm given that the last penguin arrived 7:10pm? @ (e) Given 5 penguins arrive between 7pm and 8pm, what is the probability that 3 of them arrive between 7pm and 7:20pm? 5}? (f) The tourists notice that the rate of penguins actually changes over time. While the rate is 10 penguins per hours between 7pm and 8pm it increases linearly from 10 to 20 penguins per hours at 9pm and then drops linearly to 0 at 10pm. What is the probability that exactly 30 penguins arrive between 8pm and 10am? abs}