3. The "Boston" data set is a built-in dataset in the "MASS" library of R. The "Boston" data set contains information about the housing values in suburbs of Boston city. First, load the "Boston" data set into your R workspace. In Rstudio, you can click on the "Packages" tab and then on the checkbox next to MASS. Without Rstudio, type the following command in R console: data(Boston,package="MASS") To know more information about this dataset, type the following command in R console: ?Boston Then, answer the following questions based on the dataset, using R/Rstudio: a. How many rows and columns in this data set? b. How many of the suburbs in this dataset bound the Charles River? (Hint: Variable chas is a dummy variable; chas=1 means tract bounds river, 0 otherwise) You can obtain a list of suburbs bound the Charles River with the command: subset(Boston,chas==1) You can obtain a count of the suburbs bound the Charles River by sum(Boston$chas==1) c. What is the probability that you randomly select a suburb that bounds the Charles River? 7. Suppose that A and B are two events such that P(A)=0.7, and P(B)=0.2. a. Is it possible that P(ANB) = 0.1? b. What is the smallest possible value for P(ANB)? Why? c. Is it possible that P(ANB) = 0.8? Why or why not? d. What is the largest possible value for P(ANB)? 8. A certain company sends 50% of its overnight mail parcels via express mail service E1. Of these parcels, 1% arrive after the guaranteed delivery time (denote the event late delivery by L). Suppose that 10% of the overnight parcels are sent via express mail service E2 and the remaining 40% are sent via E3. Of those sent via E2 only 2% arrive late, whereas 5% of the parcels handled by E3 arrive late. a. Draw a tree diagram for this problem. b. If a record of an overnight mailing is randomly selected from the company's file, what is the probability that the parcel went via E2 and was late? c. What is the probability that a randomly selected parcel arrived on time? d. If a randomly selected parcel has arrived late, what is the probability that is was not sent via E1?