I'm trying to work out a question from my textbook - any small tips or hints would be greatly appreciated!
If tornadoes hit a region according to a Poisson process with $\lambda = 2$, and the number of insurance claims filed after any tornado follows a Poisson distribution with mean 30, then what is the expectation of the total number of claims filed by time t?
\begin{align} \text{Since $N_t$ has a Poission distribution, then} \ E(N_t)=\lambda t \end{align} This means that we expect about 2t torando hits in time t. Since the file claims also follows a poisson distribution with mean 30,
\begin{align} E(\text{number of claims})=\lambda*\text{number of hits in time t} \end{align}
Then, $E(\text{number of claims})=60t$.
Is my reasoning wrong? I'm not really sure how to approach this problem! Thanks a ton in advance