Question

5 Boutique Store Consider a boutique store in a busy shopping mall. Every hour, a large number of people visit the mall, and each independently enters the boutique store with some small probability. The store owner decides to model X, the number of customers that enter her store during a particular hour, as a Poisson random variable with mean 2. Suppose that whenever a customer enters the boutique store, they leave the shop without buying anything with probability p. Assume that customers act independently, i.e. you can assume that they each flip a biased coin to decide whether to buy anything at all. Let us denote the number of customers that buy something as Y and the number of them that do not buy anything as Z (so X -Y +Z) (a) What is the probability that Y k for a given k? How about PIZ- k]? Hint: You can use the identity er k! (b) State the name and parameters of the distribution of Y and Z. (c) Prove that Y and Z are independent.

Please answer all parts a-c. Thanks.

Answer 1

given hat the Probabil is y k heslooe ke- is the foission distaibhin ancey

State he arte and Pasunete of He

Z. then y 42에e independent hence fovea