The Poisson distribution and its conditions Problem set B Answers

Cars pass independently of each other; at a constant average rate through the minute; one at a time.

1. (a) Yes: X ~ Po(12)
2. (b) No: X counts hours, and there is a fixed number (8) of them
3. (c) No: X is a time, not a number of cyclists
4. (d) Yes: X ~ Po(12)

1. (a) The rate is not constant: it is higher during the dinner rush than later
2. (b) The events are not independent: a stomach bug spreads from pupil to pupil
3. (c) The events do not occur singly: friends arrive together

1. (a) X ~ Po(3.1)
2. (b) Storms bring down several trees together, so the events are not independent. The model can still be useful.

1. (a) No: X counts hours (intervals), and there is a fixed number of them
2. (b) Y ~ Po(2)

1. (a) No: X is a length, not a number of flaws
2. (b) W ~ Po(4)

1. (a) X ~ B(30, 1/6)
2. (b) X ~ Po(1.5)
3. (c) X ~ B(18, 0.07)
4. (d) X ~ Po(4)