A restaurant has two waiters. suppose that the number of customers serviced daily by each waiter can be viewed as independent Poisson random variables with parameters $\lambda$ and $\mu$. whats the probability that the two waiters together handle less than $6$ customers during the day?
I was thinking along the lines of... $$ P(X\leq 6,Y\leq 6) = P(X\leq6)\cdot P(Y\leq 6), $$ but for the probability mass function of Poisson, what would $\lambda$ be?? We are not given any data regarding the average number of customers served.