Poisson Process Fishing Problem with Solutions

In this video, we solve a Poisson process fishing problem. The problem is as follows:

The fisherman's fish catch is according to a Poisson process with a rate of 0.6 per hour. The fisherman will continue to fish for 2 hours. At the end of that time, if he has caught at least one fish, he stops. Otherwise, he continues to fish until he catches at least one fish.

We solve for the following probabilities:

The probability that he continues for more than 2 hours
The probability that the total time he spends fishing is between 2 and 5 hours
The probability that he catches at least 2 fish
The expected number of fish he catches
The expected total time he will spend fishing, if it is known that he has already been fishing for 4 hours
The video includes a step-by-step explanation of the solutions, as well as a worked-out example.