Mary lives in causeway bay and works inwanchai.From Monday to Friday morning, she can go to the workplace by tram, on foot or by MTR. In each morning, she has a probability of 0.5 by tram, 0.3 on foot and 0.2 by MTR. The tram fee is $2 and MTR fee is $3.2.Let X be the traveling fee she will spend in a morning. In this question, the traveling fee in the evening is not considered.
a. What are the expected value and variance of the traveling fee in a morning?
b. What are the expected value and variance of the traveling fee in a week?
c.What is the expected number of days that she will go to workplace not on foot in a week?
d.Suppose Mary went to the workplace on foot on Monday and Tuesday. What is the expected traveling fee for the rest of the week?