Suppose we have a random variable X that measures the amount of time between fish swimming by a particular location in a river. Y measures the total number of fish that swim by in a given length of time. The mean rate of the process is that 1 fish passes every 12 minutes.

(a) What is the distribution of X? Give parameters.

(b) What is the distribution of Y ? Give parameters.

(c) Find P(X < 1 min).

(d) Find P(Y > 2 fish per hour).

(e) Given that no fish swam by in the first 2 minutes, what is the probability that one will swim by in the next four minutes?