A shop is visited by x customers per day, where x is a Poisson rv with parameter ?. Each…

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  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.