Problem 4 (11) An owner of two small sound system stores determines the following prob- abilities for Y=the number of amplifiers sold during a weekday in her store 1 and Z=the number of amplifiers sold during a weekday in her store 2. Y : 1 2 3 0.25 0.5 0.25 0 1 Z : 0.2 0.8 Assume that Y and Z are independent random variables. Suppose that an owner buys an amplifier at the cost of $40 per amplifier for store 1 and at the cost of $60 per amplifier in store 2. An owner also has a fixed weekday cost of $50 in each store. a) Express weekday total cost from the two stores in terms of Y and Z. (2) b) What is the expected weekday total cost and what is the standard devi- ation of the weekday total cost? (6) c) What is the probability that the two stores will sell different number of amplifiers on any given weekday? (3) Hint: for a simpler computation, use the complement rule