The Poisson distribution and its conditions Problem set A Answers

Emails arrive independently of each other; at a constant average rate through the hour; one at a time.

1. (a) Yes: X ~ Po(5)
2. (b) No: X counts hours, and there is a fixed number (6) of them
3. (c) No: X is a time, not a number of texts
4. (d) Yes: X ~ Po(5)

1. (a) The rate is not constant: it is higher at breakfast and lower mid-morning
2. (b) The events are not independent: a cold spreads from person to person
3. (c) The events do not occur singly: people arrive together when a train comes in

1. (a) X ~ Po(2.4)
2. (b) The rate depends on the weather and the number of swimmers, so it is not constant. 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(3)

1. (a) No: X is a volume, not a number of particles
2. (b) W ~ Po(5)

1. (a) X ~ B(40, 0.5)
2. (b) X ~ Po(6)
3. (c) X ~ B(25, 0.04)
4. (d) X ~ Po(7)