Number of floods in a given decade is a possoin r.v. with . Also every flood has a chance of being deadly(independent of the other floods). What is the mean and variance of the number of deadly floods in a decade?
I know the expected number of floods in a decade is . Each has a chance q of being deadly. So the number of deadly floods is a binomial distribution with mean with so we get a mean of and variance
My problem is with the step of taking , I don't know whether that is valid because then I'm sort of taking expectations twice. Basically I'm not sure whether my logic was correct.
Thanks in advance for the help