The sum of two independent Poisson variables Problem set A Answers

1. (a) Z ~ Po(5.5)
2. (b) 0.171
3. (c) 0.191

1. (a) The rate is not constant: it is higher at rush hour than late at night. Cars and lorries are also affected by the same events, such as a road closure, so they are not independent.
2. (b) Cold and flu spread from person to person, so the counts are not independent, and the rate changes with the season, so it is not constant.

0.215

0.740

1. (a) Z ~ Po(31)
2. (b) 0.335
3. (c) The rate is not constant: more drinks are sold at lunchtime than mid-afternoon. Hot and cold sales are not independent: on a hot day cold sales rise and hot sales fall.

1. (a) 11.5
2. (b) 3.39
3. (c) 0.625

1. (a) 4.5
2. (b) 0.175