Assignment:
A shop is visited by x customers per day, where x is a Poisson rv with parameter λ. Each customer, independently of the others, purchases a random number g of items, with g having PMD pg(k) = y(1-y)k, k= 0,1,.... The cost c of an item can be modeled as an exponential rv with parameter µ. However, when a customer buys more than G items, he/she gets a d percent discount on the bill. Determine:
a) The mean number of paying customers.
b) The mean number of sold items.
c) The mean outlay for any customer.
d) The probability that a customer spends more than S units of currency.