Question

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.

1. 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

x	0	1	2	3	4	5
P(X=x)	0.05	0.10	0.20

2. The magazines cost $4.00 per copy for the owner of the newsstand and are sold for $6.00 per copy to the customers. At the beginning of each week, the owner of the newsstand buys 6 magazines to sell during the week. 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?

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

Answer 1

a)

The distribution of X is as follows

X	0	1	2	3	4	5	6
P(X=x)	0.05	0.1	0.2	0.3	0.2	0.1	0.05

So initially we will find out the epxected value of X

Hence the expected demand is 3 magazines per week

b) So the expected amount that the seller will take in form of sales per week is equal to

As the expected number of magazine sold is 3 and selling price is 6 so expected amount after sales is $18.

c) As the expected number of the demand of magazine per week is 3 it is a waste to buy 6 magazines and if we look at the price the expected value after sales for a week is $18 and the seller would spend 4*6=$24 to buy the magazines so he would be in loss.

This isthe reason it iss not wise to buy 6 magazines.