I have a question in which I am confused a bit, A shopkeeper get 'k' numbers of customers in a day which is a Poisson random variable with PMF $$P_k(k)= \frac{u^ke^{(-u)}}{k!}$$
The probability that any customer will buy from shop is 0.3. Let M be total no. of sales on given day,
- Find conditional pmf $P_{M|K}(M|K)$
- Find for K=3, P[M=2|K=3]
What I am confused is what is the ratio factor 'U' in this case? Is it the no. of customer per day, sales per day or sales per customer?
The parameter $u$ is the average number of people who visit the shop every day. (Note that most of these people don't buy anything.)