As an acturial student, I have to do :
Show that for any two random variables V, W one has
Var(W) = E(Var(W|V )) + Var(E(W|V )).
Use the formula to solve the following problem: In a tourist office trips are organized at days with sunny weather only. Assume that on each day the weather is sunny with probability 0.7, independent of the other days. If a new guide starts to work on a sunny day, and if this guide faces N consecutive sunny days, the total number of customers until the first non-sunny day is Poisson distributed with parameter 5N, what is the expectation and variance of total customers that this guide faces until the first non-sunny day?
Is it right to use a geometric distribution for the sunny or non-sunny day ? If not which one do I need to use ?