Can you help me with this problem, please?
In a store regularly enter customers (as a Poisson process) with rate 12/hour.
1/3 of the customers buy nothing,
1/3 spend $X, where X is exponentially distributed with mean $10,
and the other 1/3 spends $Y, where Y is exponentially distributed with mean $30.
The store is open for 8h.
Find the mean and variance of the total amount of money spent in the store in one day.