Problem 1

The demand for a certain weekly magazine at a newsstand is a discrete random variable, X.The demand never exceeds 6 magazines per week.The distribution of X is symmetric about the value of 3.

(a) The table below is intended to present the distribution of variable X.Complete the table.

x--------------0------------1---------------2----------------3---------------4-------------5--------------6

P(X = x)---- 0.05---------0.10---------- 0.20------------, --------------, -------------, --------------

(b) How many magazines should the owner of the newsstand expect to sell per week? (Show your work.)

(c) At the beginning of each week, the owner of the newsstand buys 6 magazines to sell during the week. The magazines cost $4.00 per copy for the owner of the newsstand and are sold for $6.00 per copy to the customers. In dollars, what is the expected amount of money the owner of the newsstand will take in from the sales of the magazines per week?(Show your work.)

(d)Explain briefly why it would not be wise for the owner of the newsstand to buy 6 magazines at the beginning of each week.