Birds arrive at a bird feeder according to a Poisson arrival process with a rate of 6 birds per hour. A person starts watching the feeder at time 0.
- What is the probability that the first three birds arrive at the feeder within 30 minutes?
- What is the expected time it takes for the 10th bird to arrive?
- 10% of the birds who visit the feeder are cardinals. What is the probability that the 3rd cardinal to arrive at the feeder is the 10th bird to arrive at the feeder?
- 10% of the birds who visit the feeder are cardinals. The person watching the feeder decides to continue watching the feeder until they see a cardinal. What is the probability that the person waits more than 5 hours?
