1. Data indicate that the number of traf?c accidents in Berkeley on a rainy day is a Poisson random variable with mean 9, whereas on a dry day it is a Poisson random variable with mean 3. Let X denote the number of traf?c accidents tomorrow. If it will rain tomorrow with probability 0.6, ?nd
(a) E[X];
(b) P{X = 0};
(c) Var(X).
2. The number of storms in the upcoming rainy season is Poisson distributed but with a parameter value that is uniformly distributed over (0, 5). That is, A is uniformly distributed over (0, 5), and given that A = λ, the number of storms is Poisson with mean λ. Find the probability there are at least three storms this season.