Q1. Cellular Data Plan from JT&T (48 points) JT&T is promoting Plan X to UTD students. Plan X is a pre-paid cell data plan, in which you purchase x Mb for 1 cent per Mb in advance (you can choose the value of x). There will be no reimbursement if your usage is less than x, but if you run over x, cach additional Mb will cost you 2 cents. You are not sure about the total Mb that you will use but can estimate the data usage distribution as follows: Cumulative Probability Total Usage (Mb) 1000 2000 Probability 0.2 0.2 0.2 3000 . 02 4000 5000 (a) Complete the third column of the table above. (5 points) (b) Suppose you purchased 3000Mb in advance but eventually used 4000Mb. How much do you need to pay? (10 points) () You need to decide how many Mb to purchase, i.e., the value of x, in advance in Plan X. How many Mb should you buy in advance? (11 points) (d) Suppose JT&T refunds you 0.2 cent for each Mb you did not use. How many Mb should you buy in advance? (11 points) (e) JT&T wants to encourage you to purchase 4000 Mb in advance. How much should JT&T refund you for each unused Mb? (11 points)