a. ?Draw a line graph of the pmf of ?X ?in Exercise 35. Then determine the pmf of –X and draw its line graph. From these two pictures, what can you say about V(X) and V(- X)? b. ?Use the proposition involving V( aX = b) to establish a general relationship between V(X) and V( -X). Reference exercise -35 A small market orders copies of a certain magazine for its magazine rack each week. Let X = demand for the magazine, with pmf Suppose the store owner actually pays $2.00 for each copy of the magazine and the price to customers is $4.00. If magazines left at the end of the week have no salvage value, is it better to order three or four copies of the magazine? [?Hint: ?For both three and four copies ordered, express net revenue as a function of demand ?X, ?and then compute the expected revenue.]

Solution : Step 1 : Here the market orders copy of a certain magazine for its magazine racks in each week is given. If X= demands for the magazine, with pmf We have draw graph for X and -X and also by using the proposition we have to find the relationship between V(X) and V(-X). Step 2: a) 1) By using this probability distribution we can make line graph in excel. To build this graph simply list the information in Excel, choose line plot and a presentation of just the points. It will be in the form. For finding the pmf of -X , just multiply all X values with -1. So that the pmf table will be So the line graph for -X can be draw by listing the values in excel and choose insert line plot option. The line plot of -X will be From pmf line graph of X and -X we can say that they have same degree of spread about their respective means. Which means the variance of X is equal to the variance of -X. Or V(X)=V(-X)