Problem 1 The demand for a certain weekly magazine at a newsstand is a discrete random variable, X, with an expected value of 3 magazines sold per week. Furthermore, the distribution of variable X is symmetric about the value of 3. The magazines are sold for $6.00 per copy to the customers and cost $4.00 per copy for the owner of the newsstand. At the beginning of each week, the owner of the newsstand buys 6 magazines to sell during the week.
(a) The table below is intended to present the distribution of variable X. Complete the table. Justify your values. x (value of X) 0 1 2 3 4 5 6 Probability of x 0.05 0.10 0.20
(b) In dollars, what is the expected amount of money the owner of the newsstand will take in (the gross income minus the expense mentioned above) from the sales of the magazines per week? (show your work) (hint: maybe, first, you want to present a table similar to the one above)
(c) Explain briefly why it is not wise for the owner of the newsstand to buy 6 magazines at the beginning of each week. (longwinded explanations will lower your score)
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