Hello, I have a little problem finishing this question, I'll tell you how I started and if you could help me complete it will be most appreciated....
In a supermarket there is one queue for payment. The number of items that a customer buy is a random variable with Poisson distribution with a mean of 5.5 items. The customers come one after another to pay.
What is the probability that the 5th customer will be the first to collect 2 items at most, if we know that the 15th customer is the 3rd customer to collect 2 items at most. Assume that the customers are independent.
I have started by calculating the probability of collecting 2 items at most:
I know that probably some Geometric random variable is involved now, but the condition confuse me, it doesn't sound like the lack of memory issue, or maybe I am wrong. How to solve it ?